Question

Prove that X² -X is divisible by 2for all positive integer X

Answer 1

x^2 - x = x(x-1)

These are 2 adjacent numbers.
If one number is odd, then surely the other is even(as they are adjacent numbers and odd and even numbers occur alternatively)

We also know that product of an even number and an odd number is always an even number.

So x(x-1)is divisible by 2 (as it is even)
Therefore x^2 - x is divisible by 2 for all numbers except 1.


Hope this helps.