Show that `9^(n+1)` - 8n - 9 is divisible by 64, whenever n is a positive interger.

n^7-n is divisible by 42 .

3^(2n+2)-8n-9 is divisible by 8.

Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer.

n^2 -1 is divisible by 8, if n is

49^(n)+16 n-1 is divisible by

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

Prove that 3^(2n)+24n-1 is divisible by 32 .

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

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.

Prove that (n !) is divisible by (n !)^(n-1)!