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