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

Use induction to prove that 10^(n)+3 xx 4^(n+2) +5 , is dvisible by 9, for all natural no. n.

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

By mathematical induction prove that 2^(3n) -1 is divisible by 7.

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

Show that 10^(2n)-1 is divisible by 11 for all n in N .

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N