Prove: For a,b,c positive integers, ac divides bc if and only if a divides b

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If $a$ divides $b$, then $b = a \cdot k$ for some integer $k$. Thus if you multiply both sides by $c$, we get the desired $bc = akc$.

On the other hand, if $ac$ divides $bc$, then $bc = akc$ for some integer $k$. Dividing both sides by $c$ yields the desired result.

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Updated on December 10, 2022

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  • Admin
    Admin 11 months

    Prove the biconditional statement. For $a,b,c$ positive integers, $ac$ divides $bc$ if and only if a divides $b$.