Prove that `n^(2)-n` divisible by 2 for every positive integer n.

Prove that 3^(2n)-1 is divisible by 8.

Prove the 2^(n)+6times9^(n) is always divisible by 7 for any positive integer n.

Which among the following is the least number that will divide 7^(2n)-4^(2n) for every positive integer n? [4,7,11,33]

Prove that (n !)^2 < n^n n! < (2n)! , for all positive integers n.

Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1 when divided by 25 for all positive integer n.

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N