Foundations in Number Theory and Modular Arithmetic

Apply the division algorithm for integers.

Compute the greatest common divisor (GCD) of two integers using the Euclidean algorithm.

Define modular congruence and perform arithmetic with congruences.

Perform addition and multiplication in the ring of integers modulo n (Z_n).

Verify that Z_n under addition forms a cyclic group.

Identify the group of units U(n), determine which elements have multiplicative inverses, and compute them.