Show that `n^3+(n+1)^3+(n+2)^3` is divisible by `9` for every natural number `n`.

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

prove that 4^(n)-1 is divisible by 3, for each natural number n.

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

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

For all n in N , 4^(n)-3n-1 is divisible by

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

If n in N , then 3^(2n)+7 is divisible by

For each n in N, 3^(2n)-1 is divisible by

Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

For all n in N, 3^(3n)-26^(n)-1 is divisible by