Can we conclude `(a^(2n+1) + b^(2n+1))` is divisible by (a + b)?

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

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

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

Can we conclude 10^(2n)-1 is divisible by both 9 and 11? Explain. Is 10^(2n+1)-1 is divisible by 11 or not? Explain.

If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible by

AA n in N, n^(2) (n^(4) -1) is divisible by

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

For every integer n ge 1, (3^(2n) -1) is divisible by

AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by