Using the principle of mathematical induction, prove that `(2^(3n)-1)` is divisible by `7` for all `n in N`

Using the principle of mathematical induction, prove that (7^(n)-3^(n)) is divisible by 4 for all n in N .

Using principle of mathematical induction prove that sqrt(n) =2

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Using principle of mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all nN.

using Mathematical induction,prove that 3^(2n)+7 is divisible by 8.

Using the principle of mathematical induction, prove that n<2^(n) for all n in N

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

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

Prove the following by the principle of mathematical induction: 7^(2n)+2^(3n-3)*3^(n-1) is divisible 25 for all n in N