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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

Let \(m\) and \(n\) be non-zero integers. We say that \(k\) is a common divisor of \(m\) and \(n\) if \(k|m\) and \(k|n\). The greatest common divisor of \(m\) and \(n\), denoted as \(gcd(m,n)\), is the number positive \(b\) satisfying

(i) \(b\) is a common divisor of \(m\) and \(n\), and

(ii) every common divisor of \(m\) and \(n\) is also a divisor of \(b\).

Now let \(m\), \(n\), and \(j\) be non-zero integers. Prove that \(gcd(jm,jn)=j\cdot{gcd(m,n)}\).

I'm mostly just used to writing proofs about set theory or proving formulas with induction and algebraic manipulation and stuff like that, but I have no idea how to come up with any kind of workable formula out of a proposition like this. Any help with where to start would be very appreciated