Assignment:
Prove that the equivalence relation modulo m where m is an integer, forms a ring.
Also, does this same equivalence relation form a field and why?
For this proof, you are given that [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. We also know that for any two integers, a and b, that
[a]m + [b]m = [a + b]m and
[a]m[b]m = [ab]m
Provide complete and step by step solution for the question and show calculations and use formulas.