Question

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

Answer 1

In the previous step
then we take r=q(q-1)
therefore
r is used to prove that it is a multiple of 2, so when we take rest of the LHS apart from 2 as r , we will get 2r in LHS and then we can show that it is a multiple of 2.