Complete the proof of the Chinese remainder theorem by

Chapter 4, Problem 30E

(choose chapter or problem)

Complete the proof of the Chinese remainder theorem by showing that the simultaneous solution of a system of linear congruences modulo pairwise relatively prime moduli is unique modulo the product of these moduli. [Hint: Assume that \(x\) and \(y\) are two simultaneous solutions. Show that \(m_{i} \mid x-y\) for all \(i\). Using Exercise 29 , conclude that \(\left.m=m_{1} m_{2} \cdots m_{n} \mid x-y .\right]\)

Equation Transcription:

Text Transcription:

x

y

m_{i} \mid x-y

i

m=m_{1} m_{2} \cdots m_{n} \mid x-y]