# Prove that one and only one out of any three consecutive positive integers is divisible by 3.

The problem is based on the concept of divisibility by 3.

## Answer: Out of any three consecutive positive integers only one number is divisible by 3. The proof is given below.

Let's explore the nature of multiples of 3.

**Explanation:**

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

**case1: if n is a multiple of 3**- n = 3q
- n + 1 = 3q +1 [ not divisible by 3 ]
- n + 2 = 3q + 2 [ not divisible by 3 ]

**case2: if n+1 is a multiple of 3**- n+1 = 3q
- n = 3q - 1 [ not divisible by 3 ]
- n + 2 = 3q + 1 [ not divisible by 3 ]

**case3: if n+2 is a multiple of 3**- n+2 = 3q
- n = 3q - 2 [ not divisible by 3 ]
- n + 1 = 3q - 1 [ not divisible by 3 ]