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We are first asked to square a certain number then subtract our original number from that result. This can be written as:

a^2 - a

if a is your chosen number. We can rewrite this as

a(a-1)

Consider that your starting a was an even number. (a-1) would then therefor be odd. If your starting a was odd however, (a-1) would be even.

There are multiplication rules that say if an odd number is multiplied by an even number, the result is then even (you can check this by doing 3x4, 6x7, etc etc).

Therefor, squaring an integer then subtracting by your original number will always result in an even result.