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Home » So minimum occurs at endpoint $ s = \frac12 $: - Midis

So minimum occurs at endpoint $ s = \frac12 $: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Cubes mod 8:

📌 \( 0^3 = 0 \)

📌 \( 2^3 = 0 \)

📌 \( 4^3 = 64 \equiv 0 \)

📌 \( 6^3 = 216 \equiv 0 \)

📌 So only \( n \equiv 1 \pmod{8} \) gives \( n^3 \equiv 1 \). So we require:

📌 n \equiv 1 \pmod{8}

📌 Mod 125:** Solve \( n^3 \equiv 1 \pmod{125} \)

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