Question

Show that only one out of a n , n+2 , n+4 is divisible by 3,where n is any positive interger

Answer 1

Let n be divided by 3, leaving remainder r and quotient q.... Where r=0,1,2,
Now according to Euclids Division Lemma..
N = 3q+r
When r= 0
So n= 3q
This implies that n is divisible by 3.....
When r= 1
So n= 3q+1
Adding 2 on both side..... We get
N+2= 3q+3
This implies that n+2 is divisible by 3....
When r= 2
So n=3q+2
Adding 4 on both side.
We get n+4=3q+6
Again n+4= 3(q+2)
This implies that n+4 is divisible by 3.....

Therefore we get that one and one at a time are divisible by 3...... Hence proved

I hope it helps. ....