Given `P(n):3^(2n) -1` is divisible by 8.
If `P(k)` is true then prove `P(k+1)` is true.

Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true.

Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is true, show that p(k+1) is also true

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

Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m) is true, prove that P(m+1) is also true.

Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true for all natural numbers? Justify your answer.

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

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 If P(k) is true, prove that P(k+1) is also true

Consider the statement '' 10^(2n-1)+1 is divisible by 11''. Verify that P(1) is true and prove the statement by using mathematical induction.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.

Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the statement p(1) true? justify your answer