If gcd(a,m) > 1, then ax [itex]\equiv[/itex] 1 (mod m) is impossible.
The Attempt at a Solution
There is no solution per se, only an explanation. I know that m would have to divide ax and 1. Since only 1 divides 1, the statement is impossible. But that doesn't explain how the condition, gcd(a,m) > 1, is relevant. Furthermore, if the gcd(a,m) were 1, the statement would be true. Why is it that when the gcd > 1 that the congruence is impossible?