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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 In fact, since \(8 = 2^3\), for \(n^3 \equiv 0 \pmod{8}\), \(n\) must be divisible by 2. Try small even values:

📌 If \(n \equiv 0 \pmod{2}\), then \(n^3 \equiv 0 \pmod{8}\) only if \(n \equiv 0, 2, 4, 6 \pmod{8}\), but:

📌 \(2^3 = 8 \equiv 0\)

📌 \(4^3 = 64 \equiv 0\)

📌 \(6^3 = 216 \equiv 0\)

📌 So all even \(n\) satisfy \(n^3 \equiv 0 \pmod{8}\). So condition is \(n \equiv 0 \pmod{2}\), but weâll refine later.

📌 Step 2: Solve modulo 125

📌 n^3 \equiv 888 \pmod{125}

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