Question

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

Answer 1

n+2 = 3q+2+2 =3q+4 = 3(q+1)+1 is not divisible by 3. n+4 = 3q+2+4 = 3q+6 = 3(q+2) is divisible by 3. thus one and only one out of n , n+2, n+4 is divisible by 3.