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> Prove by contradiction if $a\mid b$ then $ac\mid bc $ for $a,b,c\in\Bbb Z$
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I am having considerable difficulty with this problem. Could someone give me a step-by-step solution? Even though the problem seems simple, I cannot solve it. I am new to discrete maths: I only know direct proof and contraposition (I am trying to work on contradiction). All I know is that $a\mid b$ if for some other number $c$, we have $b = a\times c$.