Question

show that exactly one of the no n,n+2 or n+4 is divisible by 3

Answer 1

Let n be any positive integer which is divisible by 3 gives q as quotient and r as remainder !!


Then,

According to Euclid's division lemma

that is

a = bq + r

So

n = 3q + r

Where

0 ≤ r < 3

r = 0 , 1 , 2


n = 3q

n = 3q + 1

n = 3q + 2



CASE 1 :-

n = 3q

It is divisible by 3

Case 2 :-

n = 3q + 1

n + 2 = 3q + 1 + 2

= 3q + 3

It is divisible by 3


Case 3 :-

n = 3q + 2

n + 4 = 3q + 2 + 4

= 3q + 6

It is divisible by 3