Question

show that exactly one of the number n n+2orn+4 is divisable by 3

Answer 1

Take n=3q
So, numbers are 3q,3q+1,3q+2.
In this set only 3q is divisible by 3.

Now,take n=3q+1
So, numbers are 3q+1,3q+2,3q+3.
In this set only 3q+3 is divisible by 3. Since remainder is three.by Euclid's division lemma i.e. a=bq+r.
Similarly .take n= 3q+2.