`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.

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.

Show that 10^(2n-1)+1 is divisible by 11 for all natural numbers 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 using mathematical induction: -n(n+1)(n+5) is divisible by 6 for all natural numbers

If n is any natural number, then 5^(2n)-1 is always divisible by how many natural numbers ?

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

Statement -1 For each natural number n,(n+1)^(7)-n^7-1 is divisible by 7. Statement -2 For each natural number n,n^7-n is divisible by 7.