44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to show why the statement of part (a) doe not hold if (a, b) # 1. С.
44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c. (b) Provide a counterexample to show why the statement of part (a) doe not hold if (a, b) # 1. С.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 4E
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Complete 44 a.
Transcribed Image Text:14 2
44. (a) Let a, b, ceZ with (a, b) = 1 and a | bc. Prove that a c.
(b) Provide a counterexample to show why the statement of part (a) doe
not hold if (a, b) ± 1.
45. Let a, b. c. and d be positive integers. If b + d and (a, b).
(с. d)
%|
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