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.
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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