Show that one and only one out of `n ,n+2or ,n+4` is divisible by 3, where `n` is any positive integer.

Explanation

To show that one and only one out of \( n, n+2, n+4 \) is divisible by 3, where \( n \) is any positive integer, we can analyze the possible cases based on the value of \( n \) modulo 3.

### Step-by-step Solution:

1. **Consider the possible values of \( n \) modulo 3**:
- Any integer \( n \) can be expressed in one of three forms based on its remainder when divided by 3:
- Case 1: \( n \equiv 0 \mod 3 \)
- Case 2: \( n \equiv 1 \mod 3 \)
...