Question

prove that one of every three consecutive integers is divisible by three

Answer 1

Let n,n+1 and n+2 be three consecutive positive integers.

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

CASE I - When n=3q+1

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(q+1) 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

3.

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