1. The problem statement, all variables and given/known data We are supposed to prove that the addition and multiplication of congruence classes for integers are associative, commutative, and distributive. 2. Relevant equations None 3. The attempt at a solution To me, it seems like this would just be trivial as all these properties follow from the fact that we are working with integers, and integers are associative, commutative, and distributive (with both addition and multiplication). Am I on the right track here? Thanks.