Is it always possible to find a positive integer m such that a is congruent to b mod m?

Question

For any two integers a and b, is it always possible to find a positive integer m such that a ≡b mod m? Either show that it is possible or find a counterexample to show that it is not.

Answer 1

The answer is yes. Without loss of generality assume that we have a>b (if a=b then just take m=1). Then for m=a-b we have that a is equal to b modulo m.