Jsing only definition of divisibility, definition of modulo, substitution, and arithmetic, prove for arbitrary ntegers (a, b, c, d, and m) the following statement, a = b (mod m) c = d (mod m) a+c=b+d (mod m)
Jsing only definition of divisibility, definition of modulo, substitution, and arithmetic, prove for arbitrary ntegers (a, b, c, d, and m) the following statement, a = b (mod m) c = d (mod m) a+c=b+d (mod 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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![Using only the definition of divisibility, definition of modulo, substitution, and arithmetic, prove for arbitrary integers \(a, b, c, d,\) and \(m\) the following statement,
\[
\begin{align*}
a &\equiv b \pmod{m} \\
c &\equiv d \pmod{m} \\
\hline
\therefore \quad a + c &\equiv b + d \pmod{m}
\end{align*}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F233b4b28-2634-4ce7-bb56-644fea0dac02%2Fcf848b03-ec56-4f67-8c2d-8061fb72a922%2Fol7pygh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Using only the definition of divisibility, definition of modulo, substitution, and arithmetic, prove for arbitrary integers \(a, b, c, d,\) and \(m\) the following statement,
\[
\begin{align*}
a &\equiv b \pmod{m} \\
c &\equiv d \pmod{m} \\
\hline
\therefore \quad a + c &\equiv b + d \pmod{m}
\end{align*}
\]
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