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

(a) P(n):5^n-1 is an integral multiple of 5,then P(5)=……..

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

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

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

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 Prove that P(1) is true

Consider the statement '' p(n):9^n-1 is a multiple of 8''. Where n is a natural number. Is p(1) true?

Consider the statement '' p(n):9^n-1 is a multiple of 8''. Where n is a natural number. Assuming p(k) is true, show that p(k+1) is true.

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

If p(n,2)=272, find n

Given that p(n,r)=(n!)/((n-r)!) What are the values of P(5, r) and P(6, r -1)?