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Exercise A.2.16. Suppose gcd (a, n) = 1. Show that there exists b such that [a], [b]= [1]n.

Exercise A.2.16. Suppose gcd (a, n) = 1. Show that there exists b such that [a], [b]= [1]n.

Advanced Engineering Mathematics
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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Exercise A.2.16. Suppose gcd(a, n) = 1. Show that there exists b such that [a] [b]n = [1]n. 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], then gcd (a, n) = 1.
Transcribed Image Text:Exercise A.2.16. Suppose gcd(a, n) = 1. Show that there exists b such that [a] [b]n = [1]n. 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], then gcd (a, n) = 1.
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