[" 27.Prove that "n^(2)-n" is divisible by "2" for every "],[" positive integer "n" ."]

Prove that n^(2)-n divisible by 2 for every positive integer n.

Prove that n^(2)-n divisible by 2 for every positive integer n.

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

Prove that n + n is divisible by 2 for any positive integer n.

Using binomial theorem, prove that 50^(n)-49n-1 is divisible by 49^(2) for all positive integers n.

Show that n^(2)-1 is divisible by 8, if n is an odd positive integer.

Prove that x^n-y^n is divisible by x - y for all positive integers n.

Prove the 2^(n)+6times9^(n) is always divisible by 7 for any positive integer n.

If p be a natural number, then prove that, p^(n+1)+(p+1)^(2n-1) is divisible by (p^(2)+p+1) for every positive integer n.