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Give a direct proof: Let a, b, and c be integers. If a b and a | c, then a (b. c). Remember that you must use the definition of I in your proof. Suppose a, b, and c are integers and a b and a | c. By the definition of 1, b = ak₁ and c for some integers k₁ and k₂. Therefore, b c = and is an integer, so a | b. c.

Give a direct proof: Let a, b, and c be integers. If a b and a | c, then a (b. c). Remember that you must use the definition of I in your proof. Suppose a, b, and c are integers and a b and a | c. By the definition of 1, b = ak₁ and c for some integers k₁ and k₂. Therefore, b c = and is an integer, so a | b. c.

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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Give a direct proof: Let a, b, and c be integers. If a | b and a c, then a | (b. c). Remember that you must use the definition of | in your proof. Suppose a, b, and care integers and a | b and a | c. By the definition of 1, b = ak₁ and c = for some integers k₁ and k₂. Therefore, b . c = a, and is an integer, so a | b. c.
Transcribed Image Text:Give a direct proof: Let a, b, and c be integers. If a | b and a c, then a | (b. c). Remember that you must use the definition of | in your proof. Suppose a, b, and care integers and a | b and a | c. By the definition of 1, b = ak₁ and c = for some integers k₁ and k₂. Therefore, b . c = a, and is an integer, so a | b. c.
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