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Computational Number Theory-Introduction

Computational Number Theory-Introduction

Well Ordering Principle & Archimedean Property

Well Ordering Principle & Archimedean Property

Mathematical Induction-First and Second Principle

Mathematical Induction-First and Second Principle

Divisibility |Part 1| Division algorithm

Divisibility |Part 1| Division algorithm

Divisibility |Part 2| Divisor "a divides b" and its basic properties

Divisibility |Part 2| Divisor "a divides b" and its basic properties

Divisibility |Part 3| Greatest Common Divisor

Divisibility |Part 3| Greatest Common Divisor

Divisibility |Part 4| Relative Primes, Euclid's Lemma

Divisibility |Part 4| Relative Primes, Euclid's Lemma

Divisibility |Part 5| Euclidean Algorithm

Divisibility |Part 5| Euclidean Algorithm

Divisibility |Part 6| Consequences of Euclidean Algorithm

Divisibility |Part 6| Consequences of Euclidean Algorithm

Bezout's Lemma

Extended Euclidean Algorithm

Extended Euclidean Algorithm

Divisibility |Part 7| Least Common Multiple

Divisibility |Part 7| Least Common Multiple

Divisibility |Part 8| Relation of LCM and GCD

Divisibility |Part 8| Relation of LCM and GCD

Divisibility | Part 9| Linear Diophantine Equation and it's solution

Divisibility | Part 9| Linear Diophantine Equation and it's solution

Primes |Part 1| Definition and basic divisibility property

Primes |Part 1| Definition and basic divisibility property

Primes |Part 2| Fundamental Theorem of Arithmetic

Primes |Part 2| Fundamental Theorem of Arithmetic

Primes |Part 3| There are infinite primes

Primes |Part 3| There are infinite primes

Primes |Part 4| Sieve of Eratosthenes

Primes |Part 4| Sieve of Eratosthenes

Number Theory | Fermat's Numbers/ Primes

Number Theory | Fermat's Numbers/ Primes

Number Theory | Mersenne Prime

Number Theory | Mersenne Prime

Number Theory | Perfect Numbers

Number Theory | Perfect Numbers

Congruences |Part 1| Definition of Congruence

Congruences |Part 1| Definition of Congruence

Congruences |Part 2| Complete System of Residues

Congruences |Part 2| Complete System of Residues

Congruences |Part 3| Equivalence Relation & Some other Basic Properties

Congruences |Part 3| Equivalence Relation & Some other Basic Properties

Congruences | Interesting Examples

Congruences | Interesting Examples

Congruences |Part 4| Cancellation Property in Congruences

Congruences |Part 4| Cancellation Property in Congruences

Congruences | Interesting Example

Congruences | Interesting Example

Congruences |Part 5| Representation of an integer with a base

Congruences |Part 5| Representation of an integer with a base

Congruences | Binary Modular Exponentiation

Congruences | Binary Modular Exponentiation

Congruences | Part 6| Divisibility Tests

Congruences | Part 6| Divisibility Tests

Congruences | Interesting Examples

Congruences | Interesting Examples

Congruences | An Interesting Example

Congruences | An Interesting Example

Congruences | Interesting Example

Congruences | Interesting Example

Congruences |Part 7| Linear Congruence and its solution

Congruences |Part 7| Linear Congruence and its solution

Congruences | Solution of some Linear Congruences

Congruences | Solution of some Linear Congruences

Congruences |Part 8| Chinese Remainder Theorem

Congruences |Part 8| Chinese Remainder Theorem

Congruence | Linear Congruence Solution | Example

Congruence | Linear Congruence Solution | Example

Congruences | System of Congruences in Two variables

Congruences | System of Congruences in Two variables

Congruences | Part 9| Fermat's Theorem

Congruences | Part 9| Fermat's Theorem

Congruences|Part 10| Another interesting result due to Fermat's Theorem

Congruences|Part 10| Another interesting result due to Fermat's Theorem

Congruences| Part 11| Wilson's theorem and its converse

Congruences| Part 11| Wilson's theorem and its converse

Congruences | Wilson Theorem | An Interesting Example

Congruences | Wilson Theorem | An Interesting Example

Congruences | A trivial non-linear Congruence solution

Congruences | A trivial non-linear Congruence solution

Euler Totient/Phi Function-Part 1

Euler Totient/Phi Function-Part 1

Euler Totient/Phi Function-Part 2

Euler Totient/Phi Function-Part 2

Euler Totient/Phi Function-Part 3

Euler Totient/Phi Function-Part 3

Euler Totient/Phi Function-Part 4

Euler Totient/Phi Function-Part 4

Euler Totient/Phi Function-Part 5

Euler Totient/Phi Function-Part 5

Euler Totient/Phi Function-Part 6

Euler Totient/Phi Function-Part 6

Primitive Roots and Indices- Lecture 1

Primitive Roots and Indices- Lecture 1

Primitive Roots and Indices-Lecture 2

Primitive Roots and Indices-Lecture 2

Primitive Roots and Indices-Lecture 3

Primitive Roots and Indices-Lecture 3

Primitive Roots and Indices-Lecture 4

Primitive Roots and Indices-Lecture 4

Primitive Roots and Indices- Lecture 5 (How to test for primitive roots.)

Primitive Roots and Indices- Lecture 5 (How to test for primitive roots.)

Lagrange's Theorem (Number of Solutions of a Polynomial Congruence)

Lagrange's Theorem (Number of Solutions of a Polynomial Congruence)

Primitive Roots and Indices-Lecture 6

Primitive Roots and Indices-Lecture 6

Primitive Roots and Indices-Lecture 7

Primitive Roots and Indices-Lecture 7

Primitive Roots and Indices-Lecture 8

Primitive Roots and Indices-Lecture 8

Primitive Roots and Indices-Lecture 9

Primitive Roots and Indices-Lecture 9

Primitive Roots & Indices - Lecture 10

Primitive Roots & Indices - Lecture 10

Primitive roots & Indices-Lecture 11

Primitive roots & Indices-Lecture 11

Quadratic Residue (Part-1) Solution of Quadratic Congruence

Quadratic Residue (Part-1) Solution of Quadratic Congruence

Quadratic Residue (Part-2) Definition of Quadratic Residue

Quadratic Residue (Part-2) Definition of Quadratic Residue

Quadratic Residue(Part-3) Euler's Criterion to check Quadratic Residue

Quadratic Residue(Part-3) Euler's Criterion to check Quadratic Residue

Quadratic Residue (Part-4) Legendre's Symbol and its basic properties

Quadratic Residue (Part-4) Legendre's Symbol and its basic properties

Quadratic Residue (Part-5) Legendre Symbol Property

Quadratic Residue (Part-5) Legendre Symbol Property

Quadratic Residue (Part-6) Gauss Lemma

Quadratic Residue (Part-6) Gauss Lemma

Quadratic Residue (Part-7) Legendre Symbol (2/p)

Quadratic Residue (Part-7) Legendre Symbol (2/p)

Quadratic Residue (Part 8) Germain Prime and its primitive roots

Quadratic Residue (Part 8) Germain Prime and its primitive roots

Quadratic Residue (Part 9) Infinite Primes of the form 4k+1 and 8k-1

Quadratic Residue (Part 9) Infinite Primes of the form 4k+1 and 8k-1

Quadratic Residue (Part 10) Lemma-Quadratic Reciprocity Law

Quadratic Residue (Part 10) Lemma-Quadratic Reciprocity Law

Quadratic Residue (Part 11) Quadratic Reciprocity Law

Quadratic Residue (Part 11) Quadratic Reciprocity Law

Quadratic Residue (Part 12) Applications-Quadratic Reciprocity Law

Quadratic Residue (Part 12) Applications-Quadratic Reciprocity Law

Quadratic Residue (Part 13) Quadratic Congruence with Composite Moduli

Quadratic Residue (Part 13) Quadratic Congruence with Composite Moduli

Quadratic Residue (Part 14) Example

Quadratic Residue (Part 14) Example

Quadratic Residue | Example| Is 246 a square Mod 257

Quadratic Residue | Example| Is 246 a square Mod 257

Quadratic Residue (Part 15) | Example | Quadratic Congruence Solvable or not

Quadratic Residue (Part 15) | Example | Quadratic Congruence Solvable or not

Cryptography | Introduction

Cryptography | Introduction

Cryptography | Types of Cryptography

Cryptography | Types of Cryptography

Cryptography | Classical Cipher | Substitution Cipher Techniques

Cryptography | Classical Cipher | Substitution Cipher Techniques

Classical Cryptography | Shift Cipher

Classical Cryptography | Shift Cipher

Classical Cryptography | Affine Ciphers

Classical Cryptography | Affine Ciphers

Cryptography | Classical Cipher | Hill Cipher

Cryptography | Classical Cipher | Hill Cipher

Cryptography | Transposition Cipher | Rail Fence Technique

Cryptography | Transposition Cipher | Rail Fence Technique

Examples | Transposition Cipher

Examples | Transposition Cipher

Cryptography | Transposition Cipher | Playfair Cipher

Cryptography | Transposition Cipher | Playfair Cipher

Cryptography | Stream Cipher & Block Cipher

Cryptography | Stream Cipher & Block Cipher

Random Numbers and Mid Square Method

Random Numbers and Mid Square Method

Linear Congruential Generator Method | Random Numbers

Linear Congruential Generator Method | Random Numbers

Blum-Blum-Shub-Pseudo Random Number

Blum-Blum-Shub-Pseudo Random Number

Linear Feedback Shift Register Method For Random Sequnecs of Bits

Linear Feedback Shift Register Method For Random Sequnecs of Bits

Cryptography | RSA Setup

Cryptography | RSA Setup

A Theorem Justifying RSA setup

A Theorem Justifying RSA setup

Examples for RSA Cryptosystem

Examples for RSA Cryptosystem

Digital Signature using RSA Algorithm

Digital Signature using RSA Algorithm

Discrete Log Problem

Discrete Log Problem

Diffie Hellman Key Exchange

Diffie Hellman Key Exchange

ElGamal Public Key Cryptosystem

ElGamal Public Key Cryptosystem

Primality & Factorization | Trial Method

Primality & Factorization | Trial Method

Factorization | Fermat Factorization Method

Factorization | Fermat Factorization Method