Is `10^(2n)+1-1` is divisible by 11 or not. Explain.

4^(n) - 3n - 1 is divisible by 9

9^11 + 11^9 is divisible by

n^2-1 is divisible by 8, if n is

Is 10^1000-1 divisible by both 9 and 11?

((n+2)!)/( (n-1)!) is divisible by

(n^3-n) is divisible by 3. Explain the reason.

Using the principle of Mathematical Induction, show that 2.4^(2n+1)+3^(3n+1) is divisible by 11, forall n in N

Prove that 6^(2n)-35n-1 is divisible by 1225 for all natural numbers of n.

(1+ x)^(n) -nx -1 is divisible by (where n in N )

Is 1^(11) + 2^(11) + 3^(11) + 4^(11) divisible by 5? Explain.