If `9^(7)-7^(9)` is divisible by `2^(n)`, then find the greatest value of n, where `n in N`.

(b) P(n):7^n-3^n is divisible by 4,then find P(2) .

(a) P(n):n(n+1)(n+2) is divisible by 6,then find P(3) .

If (n!)/((n-2)!)=56 , find the value of n

Show that 9^(n+1)-8n-9 is divisible by 64.

If 3^(2n+2)-8n-9 is divisible by 'k' for all n in N is true, then which one of the following is a value of 'k'?a)8 b)6 c)3 d)12

Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove the statement using the principle of mathematical induction for all natural numbers.

10^(n) +3(4^(n+2) )+5 is divisible by (n in N): a)7 b)5 c)9 d)17

Consider the statement P(n):7^n-3^n is divisible by 4. Verify, by the method of mathematical induction, that P(n) is true for all natural numbers.

(a) P(n):2^(3n)-1 is an integral multiple of 7,then find P(1)?

Find the value of n such that (n-1)P_3 : nP_4=1:9