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what was total population of spain in 1492 - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 3^3 = 27 \equiv 0 \\

📌 4^3 = 64 \equiv 1 \pmod{9} \quad (64 - 63 = 1) \\

📌 5^3 = 125 \equiv 125 - 13\times9 = 125 - 117 = 8 \\

📌 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 \( 7 \pmod{9} \)

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