Let $a$, $b$ an element of $\mathbb{Z}$ with $a$ and $b$ not both zero and let $c$ be a nonzero integer. Prove that $$(ca,cb) = |c|(a,b)$$
Proving that $\gcd(ac,bc)=|c|\gcd(a,b)$
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elementary-number-theory
divisibility
greatest-common-divisor
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4Please don't post in the imperative mode, giving orders. If you have a question, then please *ask*. – 2011-03-06