January 23, 2017

Homework Help: Math (Proof)

Posted by Michael on Thursday, February 14, 2013 at 3:48am.

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.

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