Question

Show that exactly one of the number n, n+2,n+4 is divisible by 3

Answer 1

We applied Euclid Division algorithm on n and 3.
 a = bq +r  on putting 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.