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Home » è§£åº \(x\)ï¼\(x = 2\) - Abu Waleed Tea

è§£åº \(x\)ï¼\(x = 2\) - Abu Waleed Tea

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 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 \( oxed{263} \).

📌 Question: An epidemiologist models the spread using a function where the number of newly infected individuals on day \( n \) is the least positive integer \( x \) such that \( x^4 \equiv 1 \pmod{17} \) and \( x

📌 ot\equiv \pm1 \pmod{17} \). What is \( x \)?

📌 Solution: We seek the smallest integer \( x

📌 ot\equiv \pm1 \pmod{17} \) such that \( x^4 \equiv 1 \pmod{17} \). The multiplicative order of \( x \) modulo 17 divides 16 (since \( \phi(17) = 16 \)), and since \( x^4 \equiv 1 \), the order divides 4.

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