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Home » \( 110 = \fracn2(3n + 7) \) - Silent Sales Machine

\( 110 = \fracn2(3n + 7) \) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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k = 5(7b + 3) + 3 = 35b + 15 + 3 = 35b + 18
So \( k \equiv 18 \pmod{35} \)
Now include the third congruence: \( k \equiv 2 \pmod{9} \)
Let \( k = 35b + 18 \). Then:
35b + 18 \equiv 2 \pmod{9}
Reduce modulo 9: \( 35 \equiv 8 \mod 9 \), \( 18 \equiv 0 \mod 9 \), s...
8b \equiv 2 \pmod{9}
Multiply both sides by the inverse of 8 modulo 9. Since \( 8 \cdot 8 =...
b \equiv 8 \cdot 2 = 16 \equiv 7 \pmod{9} \implies b = 9c + 7
k = 35(9c + 7) + 18 = 315c + 245 + 18 = 315c + 263

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