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

(b)Prove by the principle of mathematical induction that 3^n>2^n.

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

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

(a)Prove by the principle of mathematical induction that log x^n=nlogx .

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Using the principal of Mathematical induction verify that P(n) is true for all natural numbers.

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

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

Consider the statement '' 7^n-3^n is divisible by 4'' Prove the statement using mathematical induction.

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

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