prove or disprove that if m and n are integers such that mn

prove or disprove that if m and n are integers such that mn = 1, then either m = 1 and n = 1, or else m = -1 and n = -1

Solution

If m or n > 1 or < 1, then, the other has to be a fraction in order that there product is 1. But since both m and n are integers,, the product of two numbers can be 1 if and only if both are 1 or both are -1.

so, m and n = 1 or m and n = -1.