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1. Suppose that a = d · k + b, where a, b, d, k are...

1. Suppose that a = d · k + b, where a, b, d, k are all integers. Prove that b is divisible by d if and only if a is divisible by d.

Let x = abc be a three-digit number with digits a, b, c (so a, b, c ∈ {0, 1, 2, . . . 9}). Prove that x is divisible by 3 if and only if a + b + c is divisible by 3.

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