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Home » It’s arithmetic: 5 cm added each month - Midis

It’s arithmetic: 5 cm added each month - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 35b + 18 \equiv 2 \pmod{9}

📌 Reduce modulo 9: \( 35 \equiv 8 \mod 9 \), \( 18 \equiv 0 \mod 9 \), so:

📌 8b \equiv 2 \pmod{9}

📌 Multiply both sides by the inverse of 8 modulo 9. Since \( 8 \cdot 8 = 64 \equiv 1 \mod 9 \), inverse is 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

📌 Thus, the smallest positive solution is when \( c = 0 \): \( k = 263 \)

📌 The smallest such \( k \) is \( oxed{263} \).

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