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

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

For any positive integer n, prove that n^(3) - n is divisible by 6.

Pick wrong one out

Find the odd one out

Let n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot

If p is a fixed positive integer, prove by induction that p^(n +1) + (p + 1)^(2n - 1) is divisible by P^2+ p +1 for all n in N .

For every positive integer n, prove that 7^n - 3^n is divisible by 4.

if n is an odd integer, then show that n^(2) - 1 is divisible by 8.

Show that the cube of any positive integer j is of the form 4m or 4m + 1 or 4m + 3 for some integer m.