Question

show that only one of the number n, n+1 and n+2 is divisible by 3

Answer 1

Sol :

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.