Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer

n^7-n is divisible:

Show that 9^(n+1) - 8n - 9 is divisible by 64, whenever n is a positive interger.

For any positive integer a, show that one and only one out of a, a + 2 and a+4 is divisible by 3.

3^(2n)+24n-1 is divisible;

Find the sum of : the first n positive integers

Prove the statement by the principle of mathematical induction : For any natural numbers n, x^n - y^n is divisible by x - y , where x and y any integers with x ne y

10^n+3(4^(n+2))+5 is divisible by (n in N)

Prove that 2^n gt n for all positive integers n.

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer

For all n in N , 3.5^(2n+1) + 2^(3n+1) is divisible by