`n^(3)-n` is divisible by 6, for each natural numbers `n ge2`

prove that n(n^(2)+5) is divisible by 6, for each natural number 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.

prove using mathematical induction: -n(n+1)(n+5) is divisible by 6 for all natural numbers

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

n^(3)+2n divisible by

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.

Shwo that n^3+(n+1)^3+(n+2)^3 is divisible 9 for everynatural number n.