Question

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

Answer 1

Any positive integer is of the form 2q or 2q+1, for some integer q

let n = 2q

n²-n = (2q)²-2q

= 2q(2q-1)

2m,when m=q(2q-1)

Which is divisible by 2

n = 2q+1

n²-n = (2q+1)(2q+1-1)

= 2q(2q+1)

2m, when m=q(2q+1)

Which is divisible by 2 hence ,n²-n is divisible by 2 for every positive integer n