Question

Prove that x2 – x is divisible by 2 for all positive integer x.

Answer 1

${x}^{2} - x \\ = x(x - 1)$
Now these are two consecutive numbers, which means that one of the two numbers is odd and the other is even, and we all know that every even number is divisible by 2. Thus we can conclude that the given number is divisible by 2 for all integer values of x.

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