Question

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

Answer 1

n²-n can be written as n(n-1)
For every +ve integer n,

1st case :-
If n is even, (n-1) will be odd
So n(n-1) will be a even number and can be divisible by 2
(even*odd =even)

2nd case :-
If n is odd , (n-1) will be even
And n(n-1) will be a even number and can be divisible by 2
(Odd*even=even )

Here n or (n-1) will be even, hence n(n-1) will be even and can be divisible by 2