Proving Congruence For Fun

Background I want to understand the math behind asymmetric cryptography.1 This field relies heavily on Modular Arithmetic.2 I bought an undergraduate math textbook for self-study. This article is a record of a proof exercise in the book. It is also a good exercise in writing math equations using LaTeX. NOTE: I asked ChatGPT to confirm the proof. No grades are being assigned here, the point is to learn. Problem Let \(m\geq1\) be an integer.