Show that `2^(4n+4)-15n-16`, where `n in N` is divisible by 225.

Show that x^n-1 is divisible by x-1

Show that 9^(n+1)-8n-9 is divisible by 64.

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

Prove that 33 ! is divisible by 2^(15) . What is the largest integer n such that 33 ! is divisible by 2^(n) ?

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

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

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

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

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