Question

Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3.

Answer 1

a = bq +r  a = n and b = 3
n = 3q +r  , 0<r<3
i.e n = 3q   -------- (1),

n = 3q +1 --------- (2),

n = 3q +2  -----------(3)

n = 3q is divisible by 3
or n +2  = 3q +1+2 = 3q +3

also divisible by 3

or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3
Hence n, n+2 , n+4 are divisible by 3.