If n is a positive integer, show that, `9^(n+1)-8n-9` is always divisible by 64.

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

For every positive integer n, prove that 7^(n) – 3^(n) is divisible by 4.

If ninN,"then "3^(2n+2)-8n-9 is divisible by

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

By mathematical induction show that 7^(2n)+16n-1 is divisible by 64.

Show that 5^(2n) -1 is divisible for all n in N by 24.

Show that 10^(2n)-1 is divisible by 11 for all n in N .

Use the Principle of Mathematical Induction to verify that, for n any positive integer, 6 ^n −1 is divisible by 5 .