For any positive integer `n,3^(2n)+7` is divisible by 8 . Prove by mathematical induction .

Show that for any positive integer 3^(2n+2)-8n-9 is divisible by 64 .

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

If nge3 is an integer, prove by mathmatical induction that, 2n+1lt2^(n) .

Prove by mathematical induction that for any positive integer n , 3^(2n)-1 is always divisible by 8 .

Using binomial theorem for a positive integral index, prove that (2^(3n)-7n-1) is divisble by 49, for any positive integer n.

Using mathematical induction prove that for every integer nge1,(3^(2^(n))-1) is divisible by 2^(n+2) but not by 2^(n+3) .

If n (> 1)is a positive integer, then show that 2^(2n)- 3n - 1 is divisible by 9.

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

If (2^(3n)-1) is divisible by 7, then prove that, [2^(3(n+1))-1] is also divisible by 7.

P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisible by -