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Yes, it's always odd, and here's the proof:

All odd numbers can be expressed as 2p + 1, where p is any integer.

Multiply two of those together:

(2n + 1)(2p + 1) = 4np + 2n + 2p + 1 = 2(np + n + p) + 1.

Since both np, n, and p are integers, that means np + n + p is an integer; and since that integer is being multiplied by 2, it must be even. Thus, by adding 1 to that even number, the result will be odd.

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14y ago

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