real numbers

Prove that n^2 – n is divisible by 2 for every positive integer n.
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1 Answer

n2-n=n(n-1). If m is any integer, then, if even n=2m, this becomes 2m(2m-1) which is divisible by 2.

If odd n=2m+1, this becomes (2m+1)2m which is also divisible by 2.

Since all whole numbers are either odd or even n2-n is always divisible by 2.

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