I am self studying Apostol Dirichlet series and Modular functions in number theory and I am struck on Ch -2 Problem 17. It is a problem of elementary number theory but I am not able to think about it.
Question: if a, b, n are integers with n greater than or equal to 1 and ( a, b, n) =1 , then prove that the congruence ax- by=1 ( mod n) has exactly n solutions, distinct mod n.
I tried using solutions of diophantine equation ax+by= c but can't do it. Please help