SOLUTION: prove that the square of an even number is always even and the square of an odd number is always odd

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Question 476562: prove that the square of an even number is always even and the square of an odd number is always odd
Answer by robertb(5830) About Me  (Show Source):
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%282n%29%5E2+=+4n%5E2+=+2%282n%5E2%29, so the square of an even number is always even.
%282n%2B1%29%5E2+=+4n%5E2+%2B+4n+%2B+1+=+2%282n%5E2+%2B+2n%29+%2B+1, so the square of an odd number is always odd.