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

**Case 1:** Let n is divisible by 3

So n = 3k for some positive integer k

Now n+2 = 3k+2 which is not divisible by 3

n+4 = 3k +3+1 =3(k+1)+1 =3m+1 not divisible by 3

**Case 2:** n+2 is divisible by 3 so

n+2 =3k

so n =3k-2 not divisible by 3

n+4 = 3k+2 = not divisible by 3

**Case 3:** Let n+4 is divisible by 3 so n+4 = 3k

n =3k-4=3(k-1)-1=3m-1 not divisible by 3

n+2 = 3k-2 not divisible by 3