Using binomial theorem prove that `4^n -3n-1` is divisible.by 9 for `n in N`

(n^2-1) is divisible by 8,if n is

For n in N prove that 5^n+2.3^(n-1)+1 is divisible by 8.

Prove by the principle of mathematical induction that for all n in N. (2^(3n)-1) is divisible by 7 for all n in N .

Prove by the principle of mathematical induction that for all n in N. 5^(2n)-1 is divisible by 24 for all n in N .

Prove by the principle of mathematical induction that for all n in N. 3^(2n)+7 is divisible by 8 for all n in N .

Prove by the principle of mathematical induction that for all n in N. (10^(2n-1)+1) is divisible by 11 for all n in N .

Prove by mathematical induction 2^(3n)-1 is divisible by 7.

Prove by the principle of mathematical induction that for all n in N. Sn=n^3+3n^2+5n+3 is divisible by 3 for all n in N

If n is a natural number ,then 9^(2n)-4^(2n) is always divisible by a)5 b)13 c)both 5 and 13 d)None of these

Find the value of .^(n-1)C_(n-1)