Exercise A.2.17. (1) Show that gcd(a,n) = 1 if and only if there exist m and k such that ma + kn = 1. (2) Use part (1) to prove that if there b such that [a], · [b]n = [1]n, then gcd(a, n) = 1.
Exercise A.2.17. (1) Show that gcd(a,n) = 1 if and only if there exist m and k such that ma + kn = 1. (2) Use part (1) to prove that if there b such that [a], · [b]n = [1]n, then gcd(a, n) = 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 51E
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Question
![Exercise A.2.17. (1) Show that gcd(a,n)
= 1 if and only if there exist m and k such that ma + kn =
1.
(2) Use part (1) to prove that if there is b such that [a]n · [b]n = [1]n, then gcd (a,n) = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c99a240-9de7-4947-9b54-53ff2cf6c85e%2F0fc624ef-80ec-4556-8c17-a207a32648ee%2Feya3a3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise A.2.17. (1) Show that gcd(a,n)
= 1 if and only if there exist m and k such that ma + kn =
1.
(2) Use part (1) to prove that if there is b such that [a]n · [b]n = [1]n, then gcd (a,n) = 1.
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