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2.18. Solve each of the following simultaneous systems of congruences (or explain why no solution exists). (a) x = 3 (mod 7) and x = 4 (mod 9). (b) x = 137 (mod 423) and x = 87 (mod 191). (c) x 133 (mod 451) and x = 237 (mod 697). (d) x = 5 (mod 9), x = 6 (mod 10), and x = 7 (mod 11). and x = 18 (mod 71). (e) x 37 (mod 43), x = 22 (mod 49), and

2.18. Solve each of the following simultaneous systems of congruences (or explain why no solution exists). (a) x = 3 (mod 7) and x = 4 (mod 9). (b) x = 137 (mod 423) and x = 87 (mod 191). (c) x 133 (mod 451) and x = 237 (mod 697). (d) x = 5 (mod 9), x = 6 (mod 10), and x = 7 (mod 11). and x = 18 (mod 71). (e) x 37 (mod 43), x = 22 (mod 49), and

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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### 2.18. Solve each of the following simultaneous systems of congruences (or explain why no solution exists). (a) \( x \equiv 3 \pmod{7} \) and \( x \equiv 4 \pmod{9} \). (b) \( x \equiv 137 \pmod{423} \) and \( x \equiv 87 \pmod{191} \). (c) \( x \equiv 133 \pmod{451} \) and \( x \equiv 237 \pmod{697} \). (d) \( x \equiv 5 \pmod{9} \), \( x \equiv 6 \pmod{10} \), and \( x \equiv 7 \pmod{11} \). (e) \( x \equiv 37 \pmod{43} \), \( x \equiv 22 \pmod{49} \), and \( x \equiv 18 \pmod{71} \).
Transcribed Image Text:### 2.18. Solve each of the following simultaneous systems of congruences (or explain why no solution exists). (a) \( x \equiv 3 \pmod{7} \) and \( x \equiv 4 \pmod{9} \). (b) \( x \equiv 137 \pmod{423} \) and \( x \equiv 87 \pmod{191} \). (c) \( x \equiv 133 \pmod{451} \) and \( x \equiv 237 \pmod{697} \). (d) \( x \equiv 5 \pmod{9} \), \( x \equiv 6 \pmod{10} \), and \( x \equiv 7 \pmod{11} \). (e) \( x \equiv 37 \pmod{43} \), \( x \equiv 22 \pmod{49} \), and \( x \equiv 18 \pmod{71} \).
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