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Prove the following theorem: For every integer n, there is an even integer k such that...

Prove the following theorem: For every integer n, there is an even integer k such that

n ≤ k+1 < n + 2.

Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.

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