Question

Prove that any positive integer and its square ara even numbers.​

Answer 1

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The sum of an integer x and its square is x2 + x. Now, since x is either even or odd, there is some integer k such that either x = 2k if x is even or x = (2k + 1) if x is odd. If x = 2k, then x2 + x = (2k)2 + 2k, which equals 4k2 + 2k, which by factoring equals 2(2k2 + k), which is even.

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Answer 2

Answer:

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