Question

Prove that for all integers a, b, c if a|b then ac|bc

Answer 1

ANSWER on Question #85798 – Math – Discrete Mathematics

QUESTION

Prove that for all integers $a, b, c$ if $a|b$ then $ac|bc$.

SOLUTION

Notation $a|b$ means that there exists an integer $k$ such that

$$ka = b$$

We can multiply the last equality $ka = b$ by any integer $c$ and the equality will not change.

Then,

$$ka = b \mid \times (c) \rightarrow cka = cb \rightarrow k(ac) = bc \rightarrow ac|bc$$

Q.E.D.

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