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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Q: x and y. Prove that if alb and alc, then a|(xb+ yc) for any integers

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Q: For all a be a, a=gal cabl id and only it acdinde b

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Q: Prove the following statement in three different ways, using a direct proof, a contrapositive proof…

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Q: Prove that if a < 1 and [b] < 1. a -b = 201₁ āb 1 <1

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Q: Let i, r, and k be positive integers, and let s gcd(i, r). Assume that r | ik. Prove that | k.

A: To prove the divisibility property under the given conditions