congruences: Prove a is congruent to b, mod m, given that...

[gigiserio]

Suppose that ac congruence bc (mod m) and also that gcd (c,m) = 1. Prove that a congruence b ( mod m).

 

[royhaas]

The congruence is equivalent to $\displaystyle c(a-b)=km$ for some integer $\displaystyle k$.