Integer just greater tehn `(sqrt(3)+1)^(2n)` is necessarily divisible by (A) `n+2` (B) `2^(n+3)` (C) `2^n` (D) `2^(n+1)`

10^n+3(4^(n+2))+5 is divisible by (n in N)

2^(2n)-3n-1 is divisible by ........... .

Prove by induction that the integer next greater than (3+sqrt(5))^n is divisible by 2^n for all n in N .

if n is an odd integer, then show that n^(2) - 1 is divisible by 8.

For any positive integer n, prove that n^(3) - n is divisible by 6.

For all n in N , 3.5^(2n+1) + 2^(3n+1) is divisible by

3^(2n)+24n-1 is divisible;

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

If n is an odd integer greater than or equal to 1, then the value of n^3 - (n-1)^3 + (n-2)^3 - (n-3)^3 + .... + (-1)^(n-1) 1^3

If p is a fixed positive integer, prove by induction that p^(n +1) + (p + 1)^(2n - 1) is divisible by P^2+ p +1 for all n in N .