`3^(2n)+9n+1` when divided by 9 will leave the remainder

6^(n)-5 n when divided by 25 leaves the remainder

Prove the following by using the Principle of mathematical induction AA n in N 3^(2n) when divided by 8 leaves the remainder 1.

For a positive integer n,n(n+1)(2n+1) when divided by 6 leaves the remainder -

9^(6)-11 when divided by 8 would leave a remainder of:

Using principle of mathematical induction, prove that 5^(n+1)+4.6^(n) when divided by 20 leaves the remainder 9, for all n in N