# Prove that one of every three consecutive positive integers is divisible by 3.

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

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

So ,we have the following cases.

Case1: When n=3q

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

Case2: 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

Case3: when n=3q+2

in this case ,n+1=3q+2+1=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 divisible by 3

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