Even If And Only If Square Is Even

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Problem 41: (Even If And Only If Square Is Even)

Let $n$ be an integer. In previous problems we have proven that the three statements below are true.

• If $n$ is not even, then $n$ is odd.
• If $n$ is odd, then $n^2$ is odd.
• If $n^2$ is odd, then $n$ is odd.

Write the contrapositive of each of these statements. Then prove that $n$ is even if and only if $n^2$ is even.

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