proof the following step by step in detail with extra emphasises on proof writing style Chinese Remainder Theorem.Let p, q be distinct primes and consider the function f: Z → Zp × Zq sen-ding a € Z to the pair ([a]p, [a]q) consisting of its congruence class modulo p and itscongruence class modulo q. Via part (a), f gives us an equivalence relation ~ on Z.Show that ab if and only if a = b (mod pq).

Answered: Image /qna-images/answer/123b2863-df46-441c-8694-34afdb101eb5.jpg

Let p, q be distinct primes and consider the function f: Z → Zp XZq sen- ding a € Z to the pair ([a]p, [a]q) consisting of its congruence class modulo p and its congruence class modulo q. Via part (a), f gives us an equivalence relation on Z. Show that ab if and only if a = b (mod pq). ~

Let p, q be distinct primes and consider the function f: Z → Zp XZq sen- ding a € Z to the pair ([a]p, [a]q) consisting of its congruence class modulo p and its congruence class modulo q. Via part (a), f gives us an equivalence relation on Z. Show that ab if and only if a = b (mod pq). ~

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 5E: 5. Let be the relation “congruence modulo ” defined on as follows: is congruent to modulo if...

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Question

proof the following step by step in detail with extra emphasises on proof writing style

Chinese Remainder Theorem.
Let p, q be distinct primes and consider the function f: Z → Zp × Zq sen-
ding a € Z to the pair ([a]p, [a]q) consisting of its congruence class modulo p and its
congruence class modulo q. Via part (a), f gives us an equivalence relation ~ on Z.
Show that ab if and only if a = b (mod pq).

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