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Home » Solutions are \( n = 20 \) or \( n = -21 \). - AMAZONAWS

Solutions are \( n = 20 \) or \( n = -21 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 L \equiv 1 \pmod{13} \quad ext{and} \quad L \equiv 0 \pmod{7}

📌 L \equiv 0 \pmod{7} \

📌 Use the Chinese Remainder Theorem. Let $ L = 7k $. Substitute into the second congruence:

📌 7k \equiv 1 \pmod{13}

📌 We solve for $ k $: find the modular inverse of 7 modulo 13.

📌 $ 7 \cdot 1 = 7

📌 $ 7 \cdot 2 = 14 \equiv 1 \pmod{13} $

📌 So $ 7^{-1} \equiv 2 \pmod{13} $

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