Question

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

Answer 1

n^2-n
n(n-1)

Now two cases are possible
1→n is even
So n is divisible by 2, hence the given number is also divisible by 2

2→n is odd
so n-1 is even, hence again the given number is divisible by 2

So in both cases n^2-n is divisible by 2