Lectures related to Fermat number

Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.

Complex Numbers: Group Morphisms and Fermat Primes

Explores group morphisms in complex numbers and the concept of Fermat primes.

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Explores the constructibility of regular polygons, Fermat numbers, historical conjectures, and the compass's fundamental role in geometric constructions.

Complex Numbers: Equations and Constructibility

Explores polynomial equations in complex numbers, constructibility conditions, roots of unity, and Fermat primes.

Prime Numbers and Primality Testing

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

RSA Cryptosystem: Encryption and Decryption Process

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

RSA Cryptography: Primality Testing and Quadratic Residues

Explores RSA cryptography, covering primality testing, quadratic residues, and cryptographic applications.

Fermat Equation: Solutions and Coprime Numbers

Explores solutions of the Fermat equation and the importance of coprime numbers.

Fermat's Little Theorem: Applications and Probabilities

Explores Fermat's Little Theorem applications and probabilities in primality testing.

Fermat's Little Theorem

Explores Fermat's Little Theorem, its extensions, primality testing algorithms, and the significance of prime numbers in cryptography.

Homomorphic Encryption: Fermat FHE

Covers fully homomorphic encryption modulo Fermat numbers and its applications.

Lenstra's Algorithm: Integer Factorization

Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.

Factorisation in PIDs

Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.

Iterative Methods for Linear Systems

Covers iterative methods for solving linear systems of equations and discusses the convergence properties of methods like Richardson's method.

Diffie-Hellmann Protocol

Explores the Diffie-Hellmann protocol for secure communication using modular arithmetic.

Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.