Question

prove that one out of every three consecutive integers is divisible by 3​

Answer 1

Step-by-step explanation:

We know that n is of the form 3q,3q+1 or, 3q+2

So, we have the following

Case I When n=3q

In this case, n is divisible by 3 but n+1 and n+2 are not divisible by 3.

Case II When n=3q+1

In this case, n+2=3q+1+2=3 is divisible by 3 but n and n+1 are not divisible by 3.

Case III When n=3q+2

In this case, n+1=3q+1+2=3(q+1) is divisible by 3 but n and n+2 are not divisible by 3.

Hence one of n,n+1 and n+2 is divisible by 3.

hence proved