(a)For every positive integer n,`7^n-3^n` should be divisible by (2,3,4,8).

For every positive integer n,prove that 7^n-3^n is divisible by 4 using principle of mathematical induction.

If n is a positive integer then 5^(2n+2)-24n-25 is divisible by

For all nge1 , prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

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

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

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

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

For all nge1 , prove that p(n):n(n+1)(n+5) is divisible by 3.

Prove that 33 ! is divisible by 2^(15) . What is the largest integer n such that 33 ! is divisible by 2^(n) ?

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.