Question

prove that n2-n is divisible by 2 for every positive integer n

Answer 1

${n}^{2} - n = n(n - 1)$
Which means for every positive integer, this equation will be the product of two consecutive integers.
Since every odd integer is followed by an even integer and vice versa, the product will always be even. So, this equation will also always be even for any positive integer.