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

Prove each of the statements by the principle of mathematical induction : n(n^2 + 5) is divisible by 6, for each natural number n.

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

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

Prove the statement by the principle of mathematical induction : n^3 - 7n+ 3 is divisible by 3, for all natural number n .

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N

Prove the statement by the principle of mathematical induction : 4^n - 1 is divisible by 3, for each natural number n .

Prove by the principle of mathematical induction that: n(n+1)(2n+1) is divisible by 6 for all n in Ndot

Using mathematical induction prove that 10^(2n-1)+1 is divisible by 11 for all n in N

Using mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all n in N

Prove the following by the principle of mathematical induction: 5^(n)-1 is divisible by 24 for all n in N.