Question

show that one and only one out of n, [n+2] or [n+4] is divisible by 3 where n∈N

Answer 1

Solution=
Case 1 =  Let n = 3q
                n + 2 = 3q + 2
               and n + 4 = 3q +4
      Here, only n is a multiple of 3
.........,etc and many more cases can be made that proves your statement..