If $a|c$ and $b|c$ and $\gcd(a,b) = 1$, prove that $ab|c$.
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1Welcome to MSE! Can you share what you've tried and explain what you're having trouble with? – Feb 09 '16 at 05:05
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I really don't know where to start right now – Matt Feb 09 '16 at 05:10
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Do you know any results about numbers and gcds? Like factorization, or Bezout's theorem, or anything? Surely this wasn't phrased as an isolated exercise from the sky.... – Feb 09 '16 at 05:10
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Yes. I know about what a GCD is and factorization – Matt Feb 09 '16 at 05:15
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3Possible duplicate of If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$ – Feb 09 '16 at 05:21
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$a|c \implies c = ka$. $b|c \implies b|ka$ but since $gcd(a,b) = 1$, $b|ka \implies b|k \implies k = db \implies c = dba \implies ab|c$.
Bob Roberts
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