Question

Prove that one and only one put of n, n+1 ,n+2 is divisible by 3

Answer 1

Answer:

Let a be any positive integer when divided by 3 q be quotient and r be remainder

By Euclid division lemma n = bq + r

3>r>=0

Possible value of r = 0,1 ,2

If r=0 then

n=3q,n+1=3q+1,n+2=3q+2 so here only n is divisible by 3

Now if r = 1

Then n= 3q+1 ,n+1 =3q+2,n+2 = 3q+3=3(q+1)

Here only 3n+2 is divisible

Now if r=2

Then n = 3q+2 ,n+1=3q+3 ,n+2 = 3q+4

Here only n+1 is divine by 3

So it is proved that only one out of n,n+1,n+2 is divisible by 3