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X = 17 (mod 21) X= - ) 8 Cmod 25

X = 17 (mod 21) X= - ) 8 Cmod 25

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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Sure! Here's a transcription suitable for an educational website: --- This section covers a system of congruences, which is part of number theory in mathematics. We are given the following two congruences: 1. \( x \equiv 17 \pmod{21} \) 2. \( x \equiv -8 \pmod{25} \) **Explanation:** - The first congruence, \( x \equiv 17 \pmod{21} \), means that when \( x \) is divided by 21, the remainder is 17. - The second congruence, \( x \equiv -8 \pmod{25} \), means that when \( x \) is divided by 25, the remainder is -8. Note that the remainder can also be expressed in positive terms as \( x \equiv 17 \pmod{25} \), since \( -8 \equiv 17 \pmod{25} \) (because \( 25 - 8 = 17 \)). These congruences can be solved using various methods, such as the Chinese Remainder Theorem, to find a common solution for \( x \). ---
Transcribed Image Text:Sure! Here's a transcription suitable for an educational website: --- This section covers a system of congruences, which is part of number theory in mathematics. We are given the following two congruences: 1. \( x \equiv 17 \pmod{21} \) 2. \( x \equiv -8 \pmod{25} \) **Explanation:** - The first congruence, \( x \equiv 17 \pmod{21} \), means that when \( x \) is divided by 21, the remainder is 17. - The second congruence, \( x \equiv -8 \pmod{25} \), means that when \( x \) is divided by 25, the remainder is -8. Note that the remainder can also be expressed in positive terms as \( x \equiv 17 \pmod{25} \), since \( -8 \equiv 17 \pmod{25} \) (because \( 25 - 8 = 17 \)). These congruences can be solved using various methods, such as the Chinese Remainder Theorem, to find a common solution for \( x \). ---
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