Question

show that one and only out of n,n+1 and n+4 divisible by 3 where n is any positive integer​

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.