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Home » What is the sum of the distinct prime factors of 360? - Databee Business Systems

What is the sum of the distinct prime factors of 360? - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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n^2 - 1 \equiv 0 \pmod{15} \implies (n-1)(n+1) \equiv 0 \pmod{15}
This means that \( (n-1)(n+1) \) is divisible by 15. Since 15 factors...
Step 1: Check modulo 3
The possible residues modulo 3 are 0, 1, and 2:
If \( n \equiv 0 \pmod{3} \), then \( n^2 \equiv 0 \pmod{3} \),
If \( n \equiv 1 \pmod{3} \), then \( n^2 \equiv 1 \pmod{3} \),
If \( n \equiv 2 \pmod{3} \), then \( n^2 \equiv 4 \equiv 1 \pmod{3} \...
Thus, \( n^2 \equiv 1 \pmod{3} \) when \( n \equiv 1 \) or \( 2 \pmod{...
Step 2: Check modulo 5
Similarly, test residues modulo 5:

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