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Home » You Won’t Believe How Kenichi The Mighty Conquered the Mythical Arena! - Aurero

You Won’t Believe How Kenichi The Mighty Conquered the Mythical Arena! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 6^3 = 216 \equiv 0 \\

📌 7^3 = 343 \equiv 343 - 38\times9 = 343 - 342 = 1 \\

📌 So \( r^3 \equiv 1 \pmod{9} \) when \( r \equiv 1, 4, 7 \pmod{9} \)

📌 Thus, \( D \equiv 1, 4, \text{ or } 7 \pmod{9} \)

📌 We exclude \( D \equiv 1 \pmod{9} \), so keep \( D \equiv 4 \) or \( 7 \pmod{9} \)

📌 Find the smallest three-digit number congruent to 4 or 7 modulo 9.

📌 Smallest three-digit number: 100

📌 \( 100 \div 9 = 11 \times 9 = 99 \), remainder 1 → \( 100 \equiv 1 \pmod{9} \) → exclude

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