posted by Michael .
Prove that if ab = ac (mod n) and a is relatively prime to n, then b = c (mod n).
Proof: a and n are relatively prime and from ab = ac(mod n), we have n|(ab-ac), so n|a(b-c). Since (a,n)=1 (relatively prime), we get n(b-c). hence b=c(mod n).
But what if a and n are not relatively prime, can you still prove ab = ac (mod n)? Can you show a counterexample if I cannot be done? Thank you.