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Proof

(related to Proposition: Product of Two Even Numbers)

Let the integers \(m, n\) be even.
By definition, $2$ is a divisor of $n$ and $m.$
Therefore $n=2k$ and $m=2l$ for some integers $k,l.$
For the product, it follows \(nm=2k\cdot 2l=2(k2l)\), because the multiplication of integers is associative.
Therefore, $2\mid nm.$
Thus, the product $nm$ is even.
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