Monday

December 22, 2014

December 22, 2014

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

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.

- Math (Proof) -
**Steve**, Thursday, February 14, 2013 at 4:24amif not relatively prime, no proof.

2*3 (mod 8) = 2*7 (mod 8)

but not 3 = 7 (mod 8)

The primeness is vital. n can divide ab-ac of the products, but if a factor of n is also factor of a, then n need not divide b-c.

- Math (Proof) -
**Michael**, Thursday, February 14, 2013 at 5:32amThank you!

**Answer this Question**

**Related Questions**

math - Which two is true as i'm confused A) 3+7 10 mod 15 17 + 9 4 mod 21 ...

Math - Which Statements of congruence are true and which are false and why? 177 ...

math - Which Statements of congruence are true and which are false and why? 177 ...

Math - Which Statements of congruence are true and which are false and why? 177 ...

Proofs and numbers - Prove the following theorem: Suppose p is a prime number, r...

discrete math - which positive integers less than 12 are relatively prime to 13 ...

A number thoery question - Please help me! Thank you very much. Prove Fermat's ...

Discrete Math - Let a, b, c, and d be integers, and let n be a positive integer...

math - how do we find the least residue of 1789 (mod 4), (mod 10), (mod 101)

math - how do we find the least residue of 1789 (mod 4), (mod 10), (mod 101)