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

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

Show that n(n + 1) (n + 2) is divisible by 6 where n is a natural number.

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

If a and b are distinct Integers, prove that a - b is a factor of a^(n) - b^(n) , whenever n is a positive integer. [Hint: write a^(n) = (a-b + b)^(n) and expand]

Prove that 7^(n) - 6n - 1 is always divisible by 36.

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.

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

Prove that 3^(2n)-1 is divisible by 8.