Let p be prime, $k \in$ N and let $a,b \in$ Z such that gcd(a,b)=1. How to prove that $p^k|ab$ if and only if $p^k|a$ and $p^k|b$? Trying: (<=) $p^k |a$ and $p^k|b$. Then $a=p^kq$ and $ b=p^kq'$ => $ab=p^kqp^kq'=p^kq''$ => $p^k|ab$
closed as unclear what you're asking by Najib Idrissi, Olivier Bégassat, Mathmo123, amWhy, user1729 Jul 31 at 11:50
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