Abstract Algebra: Theory and Applications · Problem 1.17

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · equivalence-relations-integers

Problem

Define a relation

\sim

on the integers

\mathbb{Z}

m \sim n

m

and

n

have the same remainder after division by

7

. Prove that

\sim

is an equivalence relation. What are the equivalence classes?