Prove that , `2^(2n)-3n-1` is divisible by 9 for all positive intergral values of n greater than 1 .

By the principle of mathematical induction prove that (5^(2n)-1) is always divisible by 24 for all positive integral values of n.

Prove that : 7^(2n)+(2^(3n-3))(3^(n-1)) is divisible by 25 forall n in N .

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,

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

Prove by induction that n(n+1)(2n+1) is divisible by 6 for all ninNN .

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,...