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Prove that n^2 +(n+1)^2 is always an odd number

User Memetech
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I assume
n\in\mathbb{Z} (or at least
n\in\mathbb{N}).


n^2+(n+1)^2=n^2+n^2+2n+1=2n^2+2n+1=2(n^2+n)+1

The above is always odd, because one of the factors of
2(n^2+n) is even, which makes the product even as well, and 1 is odd, and the sum of an even number and an odd number is an odd number.

User Dmitry Trifonov
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