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Prove that an integer is divisible by 2 if and only if the digit in the...

Prove that an integer is divisible by 2 if and only if the digit in the units place is divisible by 2. (Hint: Look at a couple of examples: 58 = 5 10 + 8, while 57 = 5 10 + 7. What does Lemma 1.3 suggest in the context of these examples?) (Lemma 1.3. If d is a nonzero integer such that d|a and d|b for two integers a and b, then for any integers x and y, d|(xa + yb). (In particular, d|(a + b) and d|(a - b).)

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