Let \(a\) and \(b\) be integers. Assume that \(a\) and \(b\) are even. Then \(a = 2k\) and \(b = 2l\) for some integers \(k\) and \(l\text{.}\) Now \(a + b = 2k + 2l = 2(k+l)\text{.}\) Since \(k + l\) is an integer, we see that \(a + b\) is even, completing the proof.
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