19, Obtain the eight incongruent solutions of the linear congruence 3x + 4y = 5 (moi 84 ELEMENTARY NUMBER THEORY m
19, Obtain the eight incongruent solutions of the linear congruence 3x + 4y = 5 (moi 84 ELEMENTARY NUMBER THEORY m
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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#19
![**Elementary Number Theory**
**19.** Obtain the eight incongruent solutions of the linear congruence \(3x + 4y \equiv 5 \pmod{8}\).
**20.** Find the solutions of each of the following systems of congruences:
(a)
\[
\begin{align*}
5x + 3y &\equiv 1 \pmod{7} \\
3x + 2y &\equiv 4 \pmod{7}
\end{align*}
\]
(b)
\[
\begin{align*}
7x + 3y &\equiv 6 \pmod{11} \\
4x + 2y &\equiv 9 \pmod{11}
\end{align*}
\]
(c)
\[
\begin{align*}
11x + 5y &\equiv 7 \pmod{20} \\
6x + 3y &\equiv 8 \pmod{20}
\end{align*}
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Transcribed Image Text:**Elementary Number Theory**
**19.** Obtain the eight incongruent solutions of the linear congruence \(3x + 4y \equiv 5 \pmod{8}\).
**20.** Find the solutions of each of the following systems of congruences:
(a)
\[
\begin{align*}
5x + 3y &\equiv 1 \pmod{7} \\
3x + 2y &\equiv 4 \pmod{7}
\end{align*}
\]
(b)
\[
\begin{align*}
7x + 3y &\equiv 6 \pmod{11} \\
4x + 2y &\equiv 9 \pmod{11}
\end{align*}
\]
(c)
\[
\begin{align*}
11x + 5y &\equiv 7 \pmod{20} \\
6x + 3y &\equiv 8 \pmod{20}
\end{align*}
\]
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