Prove that the product of two even numbers is an even number.

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Solution

Let x and y be even integers.
By definition of even we have that $x = 2 m$ and $y = 2 n$ .
Then the sum $x + y = 2 m + 2 n = 2 (m + n) = 2 k$ where $k = n + m$ is an integer.
Therefore sum of even number is even.

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