For all `nge1`, prove that `p(n):2.7^n+3.5^n-5` is divisible by 24.

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

For all nge1 , prove that p(n):n(n+1)(n+5) is divisible by 3.

For all nge1 , prove that p(n):n^3+(n+1)^3+(n+2)^3 is divisible by 9.

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

For every positive integer n,prove that 7^n-3^n is divisible by 4 using principle of mathematical induction.

(b) P(n):7^n-3^n is divisible by 4,then find P(2) .

Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 , where n in N

Using binomial theorem prove that 2^(3n)-7n-1 is divisible by 49, where ninN

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

For all nge1 , prove that 1^2+2^2+3^2+……….+n^2gtn^3/3