(Q15).Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer?

Let n be any positive integer

Let b = 3

By dividing algorithm rule for n and b : n = 3q + r, for m > 0,and 0 ≤ r <

The possible remainders are 0, 1, and 3

So, n = 3q , 3q+1, 3q+2, 3q+3, where q is the .

Let us consider n, n+2, n+4

Let r = 1, n+2

n = 3q + 1

n+2 = 3q +

n+3 = 3q +

Consider n+2 it is divisible by in the format of 3q+1

However only n+2 is divisible by 3 remaining are not divisible by .