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Show that one and only one out of n,( n+...

Show that one and only one out of n,( n+2) and ( n +4) is divisble by 3, where n is any positive interger.

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To show that one and only one out of \( n \), \( n + 2 \), and \( n + 4 \) is divisible by 3, where \( n \) is any positive integer, we can analyze the values of \( n \) modulo 3. ### Step-by-step Solution: 1. **Understanding the Remainders**: 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: \( n \equiv 1 \mod 3 \) ...
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