Lectures related to Integers: Sets, Maps, and Principles

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.

Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

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

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Covers the properties of division in integers and the relationship between divisibility and unique quotients.