An integer \(n\) is even when \(n = 2k\) for some integer \(k\text{.}\)
Section 3 Hidden Content and Navigation
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Definition 3.1. Even Integers.
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Theorem 3.2. Squares of Even Integers.
If \(n\) is even, then \(n^2\) is divisible by \(4\text{.}\)
Proof.
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Write \(n = 2k\text{,}\) so \(n^2 = 4k^2\text{.}\)
Example 3.3. A Hidden Example.
Take \(n = 6\text{.}\) Then \(n^2 = 36 = 4 \cdot 9\text{,}\) as the theorem promises.
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