Prove that `(n !+1)` is not divisible by any natural number between `2` and `n`

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

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

Use induction to prove that n^(3) - n + 3 , is divisible by 3, for all natural numbers n

Prove that 7^(n) - 6n - 1 is always divisible by 36.

If n is a natural number then sqrtn is

Show that n(n + 1) (n + 2) is divisible by 6 where n is a natural number.