Show that only one out of n, n+2, n+4 is divisible by 3

1.	Show that only one out of n, n+2, n+4 is divisible by 3
Answer» We applied Euclid Division algorithm on n and 3.a = bq +r on putting a = n and b = 3n = 3q +r , 0<r<3i.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 3or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3 Hence n, n+2 , n+4 are divisible by 3.

Answer»

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

on putting a = n and b = 3n = 3q +r , 0<r<3i.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 3or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3

Hence n, n+2 , n+4 are divisible by 3.

Discussion