a₁xb₁ (mod m₁) a2xb₂ (mod m₂) ax=bk (mod mk.) has a unique solution modulo M = [1 mi, provided that (aį, m₁) = 1 and (mi, mj) = 1, for i #j.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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Can you help me to show that the systhem has a unique solution.

=
has a unique solution modulo M
for i ‡ j.
a₁xb₁ (mod m₁)
a2x b₂ (mod m₂)
akx bk (mod mk.)
1 m₁, provided that (aį, m₁) :
=
1 and (mi, mj) = 1,
Transcribed Image Text:= has a unique solution modulo M for i ‡ j. a₁xb₁ (mod m₁) a2x b₂ (mod m₂) akx bk (mod mk.) 1 m₁, provided that (aį, m₁) : = 1 and (mi, mj) = 1,
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