Let a, b, and c, be integers. Suppose that c ≄ 0. Prove that a|b if and only if ac|ab.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let a, b, and c, be integers. Suppose that c ≄ 0. Prove that a|b if and only if ac|ab.

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Let a, b, and c, be integers. Suppose that c ≄ 0. Prove that a|b if and only if ac|bc. (Not ac| ab)

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why do we assume a|b and prove that way instead of ac|bc and prove back to a|b

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