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Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1

Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k.

Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.

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Q: Why is an odd number times an odd number an odd number?
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