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Solve the simultaneous system of congruences: 3x = 7 mod 11 5x 10 mod 15

Solve the simultaneous system of congruences: 3x = 7 mod 11 5x 10 mod 15

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Solve the simultaneous system of congruences: 1. \(3x \equiv 7 \pmod{11}\) 2. \(5x \equiv 10 \pmod{15}\) --- **Explanation:** This problem involves solving a system of linear congruences, which can be approached using the Chinese Remainder Theorem or other methods for solving congruences. The provided equations define two modular arithmetic conditions that x must satisfy simultaneously. To solve these, you would typically: 1. Solve each congruence individually using methods such as the Euclidean algorithm or trial and error to find an inverse if necessary. 2. Combine the results to find a common solution that satisfies both congruences. The direct solution steps might involve: - Finding a particular solution for each congruence. - Determining the general solution, if applicable, for simultaneous satisfaction. --- Please note that solving such problems requires some familiarity with modular arithmetic principles.
Transcribed Image Text:**Problem Statement:** Solve the simultaneous system of congruences: 1. \(3x \equiv 7 \pmod{11}\) 2. \(5x \equiv 10 \pmod{15}\) --- **Explanation:** This problem involves solving a system of linear congruences, which can be approached using the Chinese Remainder Theorem or other methods for solving congruences. The provided equations define two modular arithmetic conditions that x must satisfy simultaneously. To solve these, you would typically: 1. Solve each congruence individually using methods such as the Euclidean algorithm or trial and error to find an inverse if necessary. 2. Combine the results to find a common solution that satisfies both congruences. The direct solution steps might involve: - Finding a particular solution for each congruence. - Determining the general solution, if applicable, for simultaneous satisfaction. --- Please note that solving such problems requires some familiarity with modular arithmetic principles.
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