" 2.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.

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

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

Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 for all positive integers n.

Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 for all positive integers n.

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

If p is 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.