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

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

Show that 9^n+1 - 8n - 9 is divisible by 64, whenever n is a positive interger.

49^(n)+16n-1 is divisible by

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

Consider the statement P(n):9^(n)-1 is a multiple of 8, where n is a natural number i. Is P(1) true? ii. Assuming P(k) is true, show that P(k + 1) is also true.

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