7. Use the Chinese remainder theorem to solve this problem: N = 1 (mod 3) N = 4 (mod 5) N = 6 (mod 7)
7. Use the Chinese remainder theorem to solve this problem: N = 1 (mod 3) N = 4 (mod 5) N = 6 (mod 7)
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 7: Chinese Remainder Theorem**
Use the Chinese remainder theorem to solve this problem:
\[
\begin{align*}
N &\equiv 1 \pmod{3} \\
N &\equiv 4 \pmod{5} \\
N &\equiv 6 \pmod{7}
\end{align*}
\]
This problem requires finding an integer \( N \) that simultaneously satisfies the three given congruences. The Chinese remainder theorem can be used to find a solution, given that the moduli (3, 5, and 7) are pairwise coprime.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef0c28d5-7b68-4c4c-876c-a0f9b605d7e3%2Ff1af05ae-761b-4daa-b36d-cb68336fe01a%2Ftk0plri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7: Chinese Remainder Theorem**
Use the Chinese remainder theorem to solve this problem:
\[
\begin{align*}
N &\equiv 1 \pmod{3} \\
N &\equiv 4 \pmod{5} \\
N &\equiv 6 \pmod{7}
\end{align*}
\]
This problem requires finding an integer \( N \) that simultaneously satisfies the three given congruences. The Chinese remainder theorem can be used to find a solution, given that the moduli (3, 5, and 7) are pairwise coprime.
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