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Home » \( 64a + 16b + 4c + d = 85 \) - Dachbleche24

\( 64a + 16b + 4c + d = 85 \) - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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But 9 ≡ 1 mod 8, so perhaps only solutions ≡ 1 mod 8?
Wait — try \( n = 1, 9, 17, \dots \), but check modulo 125.
Better: solve \( n^3 \equiv 1 \pmod{1000} \), specifically mod 8 and m...
Mod 8:
Cubes mod 8:
\( 0^3 = 0 \)
\( 2^3 = 0 \)
\( 4^3 = 64 \equiv 0 \)
\( 6^3 = 216 \equiv 0 \)
So only \( n \equiv 1 \pmod{8} \) gives \( n^3 \equiv 1 \). So we requ...

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