2. Find all solutions of the system of congruences = 5 (mod 12), x = 8 (mod 9). 8
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2: Solving a System of Congruences**
Find all solutions of the following system of congruences:
\[
\begin{align*}
x & \equiv 5 \pmod{12}, \\
x & \equiv 8 \pmod{9}.
\end{align*}
\]
## Explanation
To solve this problem, we need to find an integer \( x \) that satisfies both congruences simultaneously. This involves using methods such as the Chinese Remainder Theorem or successive substitutions to find a common solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30761ad5-6d22-4ff4-adb6-4f166a7ab52a%2Fdc21c726-880c-4163-a3a9-32bc25c8aab0%2Fgajjhsj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2: Solving a System of Congruences**
Find all solutions of the following system of congruences:
\[
\begin{align*}
x & \equiv 5 \pmod{12}, \\
x & \equiv 8 \pmod{9}.
\end{align*}
\]
## Explanation
To solve this problem, we need to find an integer \( x \) that satisfies both congruences simultaneously. This involves using methods such as the Chinese Remainder Theorem or successive substitutions to find a common solution.
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