Let a,b,c,n be integers with n>1. If gcd(a,n)=1, ab congruences ac (mod n).

Prove b congruence c (mod n).

My proof so far:

Now I have ai + nj = 1 and ab = ac+ne for integers i,j,e.

Then I need something like b = c + nv for an integer v.

How do I go for that?

Thanks.

KK