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

Answer:

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.