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Home » 2025 Goals Revolution: From Dreams to Daily Wins—Start Now! - American Beagle Club

2025 Goals Revolution: From Dreams to Daily Wins—Start Now! - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 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...
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 \pm...
\( 101 \equiv 2 \)

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