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+1.331 = 4.641 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 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...
Find the smallest three-digit number congruent to 4 or 7 modulo 9.
Smallest three-digit number: 100

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