Euclid and Bézout: Algorithms and Theorems

This lecture covers the Euclidean algorithm, which efficiently finds the greatest common divisor (gcd) of two integers, and Bézout's identity, providing the inverse of an element in Z/mZ when gcd(a,m) = 1. The extended Euclid algorithm is also explained, along with examples and proofs related to gcd and multiplicative inverses. The concept of commutative groups, including the axioms and properties, is introduced, highlighting the importance of these structures in cryptography and channel coding.