Question

show that one of numbers n n+2, n+4 is divisible by3

Answer 1

Hi there!

I 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.

Cheers!