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Number Theory - Solving Congruence Equations - The ONE Solutions Case
 
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For System of Congruence equations - Chinese Remainder Theorem Examples 1 and 2: Example 1: https://www.youtube.com/watch?v=OB1OcmVSWLc Example 2: https://www.youtube.com/watch?v=NSpwIu2xaf4&list=PLsT0BEyocS2JaJZHRyyFcRV2KHyg5OEz8 The Many Solution case video: https://www.youtube.com/watch?v=fxwRrVcddww&t=15s The No Solution Case video: https://www.youtube.com/watch?v=HofgpkQH3-M In this video, I show you an example of a congruence equation that has ONE solution.
Views: 26419 Polar Pi
Fermat's Little Theorem examples
 
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Find the least residue (modulo p) using Fermat's Little Theorem; or find the remainder when dividing by p. We start with a simple example, so that we can easily check the answer, then look at much bigger numbers where the answers cannot be directly checked on a calculator.
Views: 232645 Maths with Jay
CHINESE REMAINDER THEOREM BY B.K. TUTORIALS
 
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CHINESE REMAINDER THEOREM BY B.K. TUTORIALS
Views: 107383 B.K. TUTORIALS
LINEAR CONGRUENCE PROBLEMS IN HINDI 🔥
 
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Linear congruence problems and solutions in hindi easy way to solve linear congruence problems. Problems on linear congruence . Linear congruence problems and solutions in hindi. NUMBER THEORY. LINEAR CONGRUENCE. Real Analysis - Integral Equations and Boundary Value Problems https://www.amazon.in/dp/8121928052?ref=yo_pop_ma_swf Ode and pde {differential equation} - Ordinary and Partial Differential Equations https://www.amazon.in/dp/9352535863?ref=yo_pop_ma_swf Intregral equation and boundary value problems - Integral Equations and Boundary Value Problems https://www.amazon.in/dp/8121928052?ref=yo_pop_ma_swf Please subscribe the chanel for more vedios and please support us.
Views: 21065 Mathematics Analysis
Congruence (Modular Arithmetic) & 5 Properties Explained with 7 Problems: Ultimate Shortcuts
 
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Modular arithmetic especially the properties of congruence are an important tool in arriving at quick solutions to a variety of problems. In this video Mayank unravels this concept of Congruence starting with the basic concepts and then explaining the 5 key properties of Congruence (≡): a+c ≡ (b+d)mod N (Remainder of Sums ≡ Sum of Remainders) a-c ≡ (b-d)mod N (Remainder of Difference ≡ Difference of Remainders) ac ≡ (bd)mod N (Remainder of Products ≡ Products of Remainders) a^e ≡ b^e mod N (Remainder of Exponent ≡ Exponent of Remainders) a/e ≡ b/e (mod N/gcd(N,e)) (However, don’t do division without writing basic equation Mayank applies these concepts to arrive at quick solutions for 7 representative problems - reducing seemingly impossible math involving large numbers to mere seconds. Some example problems from the video: Find the remainder 6^(6^(6^6 ) )/7 Find the last digit of (17)^16 There are 44 boxes of chocolates with 113 chocolates in each box. If you sell the chocolates by dozens, how many will be leftover? More Motivations – Reducing Big Number @0:08 Why Bother? – Shortcuts to Several Problems @1:10 Face of a Clock @2:05 Face of a Clock Replace 12 with 0 – Module 12 @4:38 What Happens with 7 Days? @6:20 Running the Clock Backwards @8:37 Addition and Subtraction of Congruence’s @10:54 Application of Addition – Example-1 @14:30 Multiplication in Congruence’s @18:46 Application of Multiplication – Example -2/3 @22:15 Exponentiation in Congruence’s @26:08 Application of Exponentiation Example -4/5 @27:58 Division of Congruence’s: Never Divide, Think from Basics @33:37 Combining Congruence’s @38:43 Example – 6 @40:36 Concept of Multiplicative Inverse @48:33 Summary @49:30 Next – Faster Solutions to Exponent Problems @51:05 #Inverse #Exponentiation #Dozens #Subtraction #Happen #Congruence #Arithmetic #Reducing #Motivations #Delayed #Mayank #Examrace
Views: 54634 Examrace
System of congruences, modular arithmetic
 
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Learn more math and science with brilliant.org, https://brilliant.org/blackpenredpen/ , first 200 people to sign up will get 20% off your subscription, and you can also support my channel! Thank you! Read more about CRT: https://brilliant.org/wiki/chinese-remainder-theorem/ Solution to the question: https://brilliant.org/problems/thursday-birthday/ a classic modular arithmetic problem, solving system of congruences, must know number theory basic, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 59317 blackpenredpen
Chinese Remainder Theorem - 2 (Solve Example) Cryptography and Network security in Hindi.
 
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Please Fill the form - https://docs.google.com/forms/d/1kOxvqvz1IvBMHJ3UeLecLDuK7ePKjHAvHaRcxduHKEE/edit ====================================================== Answer of your Questions Asked to me. (direct Link given below) Blogger Link - http://shalik-htd.blogspot.com/ ====================================================== Hey, friends, I upload the videos in this channel in Hindi for Engineering student of UPTU and other universities for computer science and IT (information technology) students. like share and subscribe my channel ====================================================== Install C Programming Solution Android app - https://play.google.com/store/apps/details?id=com.shalik.patel.cprogrammingsolution ====================================================== ====================================================== My Career Planning android app - https://play.google.com/store/apps/details?id=guide.mycareer.com.rec.mycareer ====================================================== ====================================================== My Android App for my College Library (An Official App Of College Library) - https://play.google.com/store/apps/details?id=jrv.library.rec.reclibrary ====================================================== How to use android application - https://www.youtube.com/watch?v=1hMZCvl-JxM ====================================================== Contact me on Facebook - https://www.facebook.com/HTD-hub-250593705388294/?ref=br_rs ====================================================== Follow me on twitter - https://twitter.com/PatelShalik ======================================================
The Math Needed for Computer Science (Part 2) | Number Theory and Cryptography
 
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If you missed part 1: https://www.youtube.com/watch?v=eSFA1Fp8jcU ►Support the Channel Patreon: https://patreon.com/majorprep PayPal: https://www.paypal.me/majorprep Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► For more information on math, science, and engineering majors, check us out at https://majorprep.com Best Ways to Contact Me: Facebook, twitter, or email ([email protected])
Views: 58057 MajorPrep
Number Theory - Solving Congruence Equations - The NO Solutions Case
 
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For System of Congruence equations - Chinese Remainder Theorem Examples 1 and 2: Example 1: https://www.youtube.com/watch?v=OB1OcmVSWLc Example 2: https://www.youtube.com/watch?v=NSpwIu2xaf4&list=PLsT0BEyocS2JaJZHRyyFcRV2KHyg5OEz8 The Many Solution case video: https://www.youtube.com/watch?v=fxwRrVcddww&t=15s The One Solution Case: https://www.youtube.com/watch?v=kXL9UKujxJo In this video, I show you an example of a congruence equation that has ONE solution. In this video, I show you an example of a congruence equation that has no solutions. I also prove why it has no solutions.
Views: 1103 Polar Pi
RSA-Cryptography 2
 
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We construct a small RSA cryptography system using basic number theoretic results, including linear congruences, Euler's function and Euler's Theorem.
Views: 61406 W Conradie
Number Theory: Diophantine Equation: ax+by=gcd(a,b)
 
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Once you know how to solve diophantine equations with a single variable, the next step in complexity is to consider equations with two variables. The simplest such equations are linear and take the form ax+by=c. Before we solve this equation generally, we need a preliminary result. We show that you can solve the equation ax+by=GCD(a,b) by performing the Euclidean algorithm, and then reverse-substituting to arrive at a single solution. Subject: Elementary Number Theory Teacher: Michael Harrison
Views: 96258 Socratica
The Chinese Remainder Theorem made easy
 
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A solution to a typical exam question. See my other videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.
Views: 303441 Randell Heyman
A number theory proof
 
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Find integer solutions a^2+b^2=4c+3 , a number theory proof or disproof. blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 84631 blackpenredpen
Fermat's little theorem | Journey into cryptography | Computer Science | Khan Academy
 
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Introduction to a key result in elementary number theory using a visualization with beads Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/fermat-primality-test-prime-adventure-part-10?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/random-primality-test-prime-adventure-part-9?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 81812 Khan Academy Labs
Intro to Chinese Remainder Theorem and Euler's Totient Theorem via a Challenging Problem
 
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Let's acquaint ourselves with two of the most important theorems in elementary number theory (and competition math like AMC/AIME) by solving an interesting problem. The only prerequisite is the basic knowledge of modular arithmetic (what it is, how it behaves under addition/multiplication, some intuition on number theory). Congratulations to Essentials of Math, Gustavo Exel, Devansh Sehta, Minh Cong Nguyen, Prathmesh, Eliot Argüello, Jack Miller, NoName, Daulian Doge, and Benjamin Wang for successfully solving this challenge question! Essentials of Math was the first person to solve the question. Your support is truly a huge encouragement. Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos! Every subscriber and every like are wholeheartedly appreciated. For more Weekly Math Challenges: https://www.youtube.com/playlist?list=PLpoKXj-PWCbaDXYHES37_zX4O-kCWxguM
Views: 8803 LetsSolveMathProblems
Chinese Remainder Theorem  | Cryptography And Network Security
 
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Step by step instructions on how to use The Chinese Remainder Theorem to solve a system of linear congruence. Visit Our Channel :- https://www.youtube.com/channel/UCxikHwpro-DB02ix-NovvtQ In this lecture we have taught about what how to solve multiplicative cipher method. Follow Smit Kadvani on :- Facebook :- https://www.facebook.com/smit.kadvani Instagram :- https://www.instagram.com/the_smit0507 Follow Dhruvan Tanna on :- Facebook :- https://www.facebook.com/dhruvan.tanna1 Instagram :- https://www.instagram.com/dhru1_tanna Follow Keyur Thakkar on :- Facebook :- https://www.facebook.com/keyur.thakka... Instagram :- https://www.instagram.com/keyur_1982 Snapchat :- keyur1610 Follow Ankit Soni on:- Facebook :- https://www.facebook.com/ankitsoni.1511 Instagram :- https://www.instagram.com/ankit_soni1511
Views: 55528 Quick Trixx
B.K. TUTORIALS SOLUTION OF CONGRUENCE EQUATION
 
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B.K. TUTORIALS SOLUTION OF CONGRUENCE EQUATION
Views: 34253 B.K. TUTORIALS
What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence
 
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Congruence, Modular Arithmetic, 3 ways to interpret a ≡ b (mod n), Number theory, discrete math, how to solve congruence, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 94263 blackpenredpen
Congruence and Fermat’s little theorem
 
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Introduction to congruence and the terminology used. Fairly basic with emphasis on the arithmetic of remainders. Examples of the addition and multiplication rules for congruence. Powers and Fermat’s little theorem. Lastly an example solved using Fermat’s little theorem.
Views: 91469 DLBmaths
Modular Arithmetic: Modulo Concept - Part 1
 
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This video clearly explains the concept of modulo in modular example. Several examples involving positive and negative dividends were given. Enjoy!!! www.modular-arithmetic.appspot.com www.samuelchukwuemeka.com
Views: 189879 Samuel Chukwuemeka
Solve a Linear Congruence using Euclid's Algorithm
 
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How to solve 17x ≡ 3 (mod 29) using Euclid's Algorithm. If you want to see how Bézout's Identity works, see https://www.youtube.com/watch?v=9PRPr6J_btM
Views: 211959 Maths with Jay
LINEAR CONGRUENCE UNIQUE SOLUTION BA BSC 1ST YEAR NUMBER THEORY TRIGONOMETRY EXERCISE 2.2 MODULO M
 
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BA BSC 1ST YEAR NUMBER THEORY TRIGONOMETRY EXERCISE 2.2 MODULO M LINEAR CONGRUENCE UNIQUE SOLUTION CHAPTER 2 EXERCISE 2.2 #BABSCMATHEMATICS#LINEAR CONGRUENCE# A+ JULANA EDUCATION HUB EDUCATING FOR BETTER FUTURE A PLUS INSTITUTE OF SCIENCE APJ INSTITUTE OF SCIENCE
Views: 5977 A Plus Julana - APJ
Perfect secrecy | Journey into cryptography | Computer Science | Khan Academy
 
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Claude Shannon's idea of perfect secrecy: no amount of computational power can help improve your ability to break the one-time pad Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/random-vs-pseudorandom-number-generators?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/case-study-ww2-encryption-machines?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 132743 Khan Academy Labs
Chinese Remainder Theorem (Solution of Congruence) Cryptography and Network security in Hindi.
 
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Please Fill the form - https://docs.google.com/forms/d/1kOxvqvz1IvBMHJ3UeLecLDuK7ePKjHAvHaRcxduHKEE/edit ====================================================== Answer of your Questions Asked to me. (direct Link given below) Blogger Link - http://shalik-htd.blogspot.com/ ====================================================== Hey, friends, I upload the videos in this channel in Hindi for Engineering student of UPTU and other universities for computer science and IT (information technology) students. like share and subscribe my channel ====================================================== Install C Programming Solution Android app - https://play.google.com/store/apps/details?id=com.shalik.patel.cprogrammingsolution ====================================================== ====================================================== My Career Planning android app - https://play.google.com/store/apps/details?id=guide.mycareer.com.rec.mycareer ====================================================== ====================================================== My Android App for my College Library (An Official App Of College Library) - https://play.google.com/store/apps/details?id=jrv.library.rec.reclibrary ====================================================== How to use android application - https://www.youtube.com/watch?v=1hMZCvl-JxM ====================================================== Contact me on Facebook - https://www.facebook.com/HTD-hub-250593705388294/?ref=br_rs ====================================================== Follow me on twitter - https://twitter.com/PatelShalik ======================================================
The prime number theorem | Journey into cryptography | Computer Science | Khan Academy
 
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How can we estimate the number of primes up to x? Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/time-space-tradeoff?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/comp-number-theory/v/trial-division-primality-test-using-a-sieve-prime-adventure-part-5?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 88872 Khan Academy Labs
Challenge: Can You Find A and B using Number Theory?
 
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Congratulations to Hizami Anuar, staffehn, Laura Kuttnig, Minh Cong Nguyen, FaTalCaT FL, Prof Bits, and attyfarbuckle for successfully solving the last week's math challenge question! Hizami Anuar was the first person to solve the question. Your support is truly a huge encouragement. Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos! Every subscriber and every like are wholeheartedly appreciated. Welcome, everyone! My channel hosts one weekly math challenge question per week (made by either myself, my family, or my friends), which will be posted every Wednesday. Please comment your proposed answer and explanation below! If you are among the first ten people with the correct answer, you will be recognized in the next math challenge video. The solution to this question and new question will be posted next Wednesday.
Views: 5313 LetsSolveMathProblems
Solving congruences, 3 introductory examples
 
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Solving congruences, 3 introductory examples, Number Theory, Modular Arithmetic, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://twitter.com/blackpenredpen, [email protected]
Views: 35604 blackpenredpen
Modular Arithmetic, Prime, Relatively Prime, Euler's Cryptography and Network security in Hindi.
 
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Please Fill the form - https://docs.google.com/forms/d/1kOxvqvz1IvBMHJ3UeLecLDuK7ePKjHAvHaRcxduHKEE/edit ====================================================== Answer of your Questions Asked to me. (direct Link given below) Blogger Link - http://shalik-htd.blogspot.com/ ====================================================== Hey, friends, I upload the videos in this channel in Hindi for Engineering student of UPTU and other universities for computer science and IT (information technology) students. like share and subscribe my channel ====================================================== Install C Programming Solution Android app - https://play.google.com/store/apps/details?id=com.shalik.patel.cprogrammingsolution ====================================================== ====================================================== My Career Planning android app - https://play.google.com/store/apps/details?id=guide.mycareer.com.rec.mycareer ====================================================== ====================================================== My Android App for my College Library (An Official App Of College Library) - https://play.google.com/store/apps/details?id=jrv.library.rec.reclibrary ====================================================== How to use android application - https://www.youtube.com/watch?v=1hMZCvl-JxM ====================================================== Contact me on Facebook - https://www.facebook.com/HTD-hub-250593705388294/?ref=br_rs ====================================================== Follow me on twitter - https://twitter.com/PatelShalik ======================================================
Solve a Linear Congruence with common factor
 
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How to solve 6x ≡ 4 (mod 10) If you want to see how to solve a linear congruence using Euclid's Algorithm, see https://youtu.be/4-HSjLXrfPs
Views: 67950 Maths with Jay
RSA Algorithm with solved example using extended euclidean algorithm | CSS series #7
 
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#rsa #deffiehellman #cryptographylectures #lastmomenttuitions Take the Full Course of Cryptography and Network Security What we Provide 1) 20 Videos (Index is given down) + More Update will be Coming Before final exams 2)Hand made Notes with problems for your to practice 3)Strategy to Score Good Marks in Cryptography and Network Scurity To buy the course click https://goo.gl/mpbaK3 if you have any query email us at [email protected] Sample Notes : https://goo.gl/Ze1FpX or Fill the form we will contact you https://goo.gl/forms/2SO5NAhqFnjOiWvi2 Cryptography and System Security Index Lecture 1 Introduction to Cryptography and Security System Lecture 2 Security Goals and Mechanism Lecture 3 Symmetric Cipher Lecture 4 Substitution Cipher Lecture 5 Transposition Cipher Lecture 6 Stream and Block Cipher Lecture 7 Mono Alphabetic Cipher Lecture 8 Poly Alphabetic Cipher Lecture 9 Diffie Hellman Lecture 10 RSA Algorithm with Solved Example Lecture 11 IDEA Algorithm Full Working Lecture 12 SHA-1 Algorithm Full Working Lecture 13 Blowfish Algorithm Full working Lecture 14 DES Algorithm Full Working Lecture 15 Confusion and Diffusion Lecture 16 AES Algorithm Full working Lecture 17 Kerberos Lecture 18 Malicious Software ( Virus and worms ) Lecture 19 DOS and DDOS Attack Lecture 20 Digital Signature Full working Explained More videos Coming Soon.
Views: 315993 Last moment tuitions
Cryptography and Solutions for Matching Problems - Micheal O. Rabin
 
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Innovations in Algorithmic Game Theory May 23rd, 2011 Hebrew University of Jerusalem First session: Micheal O. Rabin - Cryptography and Solutions for Matching Problems Session Chair: Noam Nisan.
Applying Fermat's Little Theorem
 
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Here we find a remainder using the powerful Fermat's Little Theorem.
Views: 12742 Joshua Helston
Arithmetic Geometry - solving number theoretical problems using geometrical intuition
 
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In the Department of Mathematical Sciences at Keio University, the Bannai Group, led by Professor Kenichi Bannai, is conducting research in number theory. Number theory, which deals with the properties of integers, is known as the "Queen of Mathematics." The Bannai Group is focused especially on arithmetic geometry. Arithmetic geometry utilizes methods and results from algebraic geometry. In this field, number theoretical problems are investigated via the geometric properties of geometric objects defined by algebraic equations. Q. "Humans perceive things in two ways, logically and intuitively. Logic involves calculating things precisely. On the other hand, when using intuition, especially geometric intuition, we look at a problem in a certain geometric way and immediately "know" the answer. If one asks how this can be applied to problems in number theory, for example, consider the problem of finding rational solutions of the equation x2 + y2 = 1. The problem of seeking rational solutions of an algebraic equation is a number theoretical problem. Geometry comes into the picture if one thinks of the equation x2 + y2 = 1 as expressing a unit circle. When I use the word geometric intuition, what I mean is, it is much easier to solve this problem if one thinks that the equation x2 + y2 = 1 is not simply an algebraic equation but also that it represents a circle." Using methods from arithmetic geometry, Andrew Wiles in 1995 solved the Fermat's Last Theorem, which had puzzled mathematicians for 300 years. Number theory can be applied for example to cryptography, which is an important practical application of number theory to society. Q. "Because number theory concerns integers s -- 1, 2, 3, and so on -- one might think it's a very narrow field. At first, I also imagined that number theory was a very narrow topic; I wanted to do mathematics, but number theory did not seem all that interesting. But when I learned that problems in number theory were deeply related to geometry and also to analysis through various interesting analytic functions, I realized that number theory was a very deep field related to a wide range of areas in mathematics. That's what's fascinating about number theory. Rather than being superficial, because number theory deals with integers, which is a very fundamental object of study, it is deeply related to many interesting theories in the forefront of mathematics." Since the dawn of civilization, numbers and equations were used to better understand natural phenomena. Through abstraction, mathematics has greatly expanded its range of application. The Bannai Group will continue to do research, in order to understand through logic and intuition abstract phenomena appearing in number theory.
Part 12 | Addition modulo and Multiplication modulo | Hindi | Discrete Mathematics
 
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• Counselling Guruji is our latest product & a well-structured program that answers all your queries related to Career/GATE/NET/PSU’s/Private Sector etc. You can register for the program at: https://goo.gl/forms/ZmLB2XwoCIKppDh92 You can check out the brochure at: https://www.google.com/url?q=http://www.knowledgegate.in/guruji/counselling_guruji_brochure.pdf&sa=D&ust=1553069285684000&usg=AFQjCNFaTk4Pnid0XYyZoDTlAtDPUGcxNA • Link for the complete playlist of Discrete Mathematics is: Relations:https://www.youtube.com/playlist?list=PLmXKhU9FNesTpQNP_OpXN7WaPwGx7NWsq Graph Theory: https://www.youtube.com/playlist?list=PLmXKhU9FNesS7GpOddHDX3ZCl86_cwcIn Group Theory: https://www.youtube.com/playlist?list=PLmXKhU9FNesQrSgLxm6zx3XxH_M_8n3LA Proposition:https://www.youtube.com/playlist?list=PLmXKhU9FNesQxcibunbD82NTQMBKVUO1S Set Theory: https://www.youtube.com/playlist?list=PLmXKhU9FNesTSqP8hWDncxpCj8a4uzmu7 • Links for the books that we recommend for Discrete Mathematics are: 1. Discrete Mathematics and Its Applications (Writer: Kenneth Rosen) (Publisher: McGraw Hill Education) https://amzn.to/2NV9viK 2. Graph Theory with Applications to Engineering and Computer Science (Writer: Deo Narsingh) (Publisher: Phi) https://amzn.to/2NSiwcc • Check out our website http://www.knowledgegate.in/ • Please spare some time and fill this form so that we can know about you and what you think about us: https://goo.gl/forms/b5ffxRyEAsaoUatx2 • Your review/recommendation and some words can help validating our quality of content and work so Please do the following: - 1) Give us a 5 star review with comment on Google https://goo.gl/maps/sLgzMX5oUZ82 2) Follow our Facebook page and give us a 5 star review with comments https://www.facebook.com/pg/knowledgegate.in/reviews 3) Follow us on Instagram https://www.instagram.com/mail.knowledgegate/ 4) Follow us on Quora https://www.quora.com/profile/Sanchit-Jain-307 • Links for Hindi playlists of other Subjects are: DBMS: https://www.youtube.com/playlist?list=PLmXKhU9FNesR1rSES7oLdJaNFgmuj0SYV TOC: https://www.youtube.com/playlist?list=PLmXKhU9FNesSdCsn6YQqu9DmXRMsYdZ2T OS: https://www.youtube.com/playlist?list=PLmXKhU9FNesSFvj6gASuWmQd23Ul5omtD Digital Electronics: https://www.youtube.com/playlist?list=PLmXKhU9FNesSfX1PVt4VGm-wbIKfemUWK Data Structures: https://www.youtube.com/playlist?list=PLmXKhU9FNesRRy20Hjr2GuQ7Y6wevfsc5 Computer Networks: https://www.youtube.com/playlist?list=PLmXKhU9FNesSjFbXSZGF8JF_4LVwwofCd Algorithm: https://www.youtube.com/playlist?list=PLmXKhU9FNesQJ3rpOAFE6RTm-2u2diwKn • About this video; In this video you’ll be learning about the addition modulo and the multiplication modulo. This video discusses the basic definition and some practice problems on addition and multiplication modulo and will help in clearing your concepts of them. Notes: Addition Modulo / +m : a +m b = 1) a + b, if y (a + b is less than m) 2) (a + b) – m, if (a + b ≥ m) Multiplication Modulo / ×m: a ×m b = 1) a × b, if (a × b is less than m) 2) (a × b) ٪, if (a × b ≥ m) Practice Problem: 1. Find the inverse of the elements in {2,3,5,6}, +5 2. Find the inverse of the elements in {2,3,5,6}, ×5 addition modulo n, addition modulo 4, addition modulo 2, addition modulo 6, addition modulo and multiplication modulo in hindi, addition modulo example, addition modulo table, addition modulo in discrete mathematics, addition modulo 3, addition modulo m, modulo 2 addition binary, addition modulo group theory, addition modulo and multiplication modulo, addition modulo n group, addition and multiplication modulo n, addition of modulo, group under addition modulo n, what is addition modulo, addition modulo 26, modulo 2 addition, modulo 8 addition example multiplication modulo 7, multiplication modulo table, multiplication modulo n, multiplication modulo 6, multiplication modulo p, multiplication modulo 3, multiplication modulo 15, multiplication modulo n is well defined, multiplication modulo in discrete mathematics, table de multiplication modulo, group under multiplication modulo n, multiplication modulo m, multiplication modulo n group, addition and multiplication modulo n, multiplication of modulo, group theory multiplication modulo, multiplication modulo 10, multiplication modulo 5, multiplication table modulo 7, multiplication modulo 8, group theory nptel, group theory in hindi, group theory mathematics in hindi, group theory iit jam, group theory mit, group theory lectures, group nptel, group theory mathematics nptel, group theory algebra, group theory alok sir, group theory and algebra, group theory, group theory and chemistry- symmetry elements and symmetry operations, group theory and quantum mechanics, group theory applications, group theory all lectures, group theory by jaipal, group theory bsc, group theory by jaipal vishwakarma, group theory by nptel, group theory basics,
Views: 78223 KNOWLEDGE GATE
Algebraic Structures: Groups, Rings, and Fields
 
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This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
Views: 53113 James Hamblin
Caesar Cipher Encryption and Decryption with Solved Example.
 
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This video will explain you in detail how caesar cipher encryption and decryption technique works. This video includes solved example for caesar cipher encryption and decryption algorithm on whiteboard. I had explained in detail about difficulties student might face while solving example related to caesar cipher in their examination. More videos about encryption algorithms, computer tips and tricks, ethical hacking are coming very soon so share this video with your friends. Subscribe to my youtube channel so that you can know when I upload any new video. See you all very soon in next video, have great days ahead. Thanks for watching my video. #caesar #encryption #decryption
Views: 33058 SR COMPUTER EDUCATION
Order of Integers and Primitive Roots
 
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This video shows you how to calculate the order of integers and how to find primitive roots.
Views: 19032 Cathy Frey
Introduction Solution - Applied Cryptography
 
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This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
Views: 10815 Udacity
Fermat's Little Theorem | Cryptography And Network Security | Tutorials | Cryptography
 
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In this youtube channel, we are going to teach you the basic concepts of Cryptography and Network Security. In this video, we have discussed how to solve Fermat's Little Theorem. Visit Our Channel :- https://www.youtube.com/channel/UCxik... Follow Smit Kadvani on:- Facebook :- https://www.facebook.com/smit.kadvani Instagram :- https://www.instagram.com/the_smit0507 Follow Dhruvan Tanna on :- Facebook :- https://www.facebook.com/dhruvan.tanna1 Instagram :- https://www.instagram.com/dhru1_tanna Follow Keyur Thakkar on:- Facebook:- https://www.facebook.com/keyur.thakka... Instagram :- https://www.instagram.com/keyur_1982 Snapchat :- keyur1610 Follow Ankit Soni on:- Instagram :- https://www.instagram.com/ankit_soni1511 Answers : 7^14mod13 = 10 456^17mod17 = 14 9^12mod13=1
Views: 21239 Quick Trixx
Congruence and Fermat's Theorem (Meaning of Congruence) Cryptography and Network security in Hindi.
 
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Please Fill the form - https://docs.google.com/forms/d/1kOxvqvz1IvBMHJ3UeLecLDuK7ePKjHAvHaRcxduHKEE/edit ====================================================== Answer of your Questions Asked to me. (direct Link given below) Blogger Link - http://shalik-htd.blogspot.com/ ====================================================== Hey, friends, I upload the videos in this channel in Hindi for Engineering student of UPTU and other universities for computer science and IT (information technology) students. like share and subscribe my channel ====================================================== Install C Programming Solution Android app - https://play.google.com/store/apps/details?id=com.shalik.patel.cprogrammingsolution ====================================================== ====================================================== My Career Planning android app - https://play.google.com/store/apps/details?id=guide.mycareer.com.rec.mycareer ====================================================== ====================================================== My Android App for my College Library (An Official App Of College Library) - https://play.google.com/store/apps/details?id=jrv.library.rec.reclibrary ====================================================== How to use android application - https://www.youtube.com/watch?v=1hMZCvl-JxM ====================================================== Contact me on Facebook - https://www.facebook.com/HTD-hub-250593705388294/?ref=br_rs ====================================================== Follow me on twitter - https://twitter.com/PatelShalik ======================================================
MAML, Number Theory: Modular Arithmetic
 
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This is a MAML (Maine Association of Math Leagues) problem from October 2011 (Meet 1 of 2011-12), Round 4, Problem 3: http://maml.net/problems.htm Also, this was recorded with gtk-recordMyDesktop: http://recordmydesktop.sourceforge.net/about.php The math writings were made on Emacs: https://www.gnu.org/software/emacs/ The Khan Academy modular arithmetic tutorial is here: https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/ Turn on captions to understand the audio better. Share this YouTube channel with the following link! https://bit.ly/nhmyoutubechannel Condensed Writing Solution: We must calculate the following: 23^15*47^17 modulo 5 By replacing 23 with 3 (23 is congruent to 3 modulo 5) and 47 with 2 (47 is congruent to 2 modulo 5) and splitting the modulos up over multiplication, we get the following: 3^15*2^17 modulo 5 (3^15 modulo 5)*(2^17 modulo 5) (3 modulo 5)*(3^2 modulo 5)*(3^4 modulo 5)*(3^8 modulo 5)*(2 modulo 5)*(2^16 modulo 5) 3 modulo 5 is simply 3. 3^2 modulo 5 is 9 modulo 5 which is simply 4. 3^4 (3^2)^2 which is congruent to 4^2=16 modulo 5 which is congruent to 1 modulo 5. Similarly, 3^8 is (3^4)^2 which is congruent to 1^2=1 modulo 5. 2 modulo 5 is simply 2. 2^16 is (2^8)^2 or 256^2 which is congruent to 1^2=1 modulo 5. Thus, the above expression is equal to: 3*4*1*1*2*1 modulo 5 24 modulo 5 4 ANSWER
Views: 191 Noble Mushtak
AKPotW: Primitive Root and -1 [Number Theory]
 
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If this video is confusing, be sure to check out our blog for the full solution transcript! https://centerofmathematics.blogspot.com/2019/04/advanced-knowledge-problem-of-week-4-30.html