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

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

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

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

Show that 10^(2n-1)+1 is divisible by 11 for all natural numbers n.

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

Prove the statement by the principle of mathematical induction : 3^(2n) - 1 is divisible by 8, for all natural number n.

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

Prove the statement by the principle of mathematical induction : 2^(3n) - 1 is divisible by 7, for all natural numbers n .