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Home » Find the sum of the first four test scores: - Imagemakers

Find the sum of the first four test scores: - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 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 \( 7 \pmod{9} \)

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

📌 Smallest three-digit number: 100

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