14. Show that if a, b, and c are integers such that (a, b) = 1 and c | (a+b), then (c, a) = (c, b) = 1.
14. Show that if a, b, and c are integers such that (a, b) = 1 and c | (a+b), then (c, a) = (c, b) = 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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![14. Show that if a, b, and c are integers such that (a, b) = 1 and c | (a+b), then (c, a) = (c, b) =
1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2e1c1fe-beca-46b1-8b3d-6a29ccacb3ea%2F9778c682-6456-4c81-9ee9-7acaca0d833f%2Ff3mgxh_processed.png&w=3840&q=75)
Transcribed Image Text:14. Show that if a, b, and c are integers such that (a, b) = 1 and c | (a+b), then (c, a) = (c, b) =
1.
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