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Prove or give a counterexample to the following statements. 1. Suppose a, b, and care integers such that alc and b|c. Then alb. 2. Suppose a, b, and c are integers such that alc and blc. Then (a + b)|c. 3. Suppose a, b, and c are integers such that alb. Then albc. 4. Suppose a, b, and c are integers such that alb and a|c. Then al(b + c).

Prove or give a counterexample to the following statements. 1. Suppose a, b, and care integers such that alc and b|c. Then alb. 2. Suppose a, b, and c are integers such that alc and blc. Then (a + b)|c. 3. Suppose a, b, and c are integers such that alb. Then albc. 4. Suppose a, b, and c are integers such that alb and a|c. Then al(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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Prove or give a counterexample to the following statements. 1. Suppose a, b, and c are integers such that alc and b|c. Then a|b. 2. Suppose a, b, and c are integers such that alc and b|c. Then (a + b)|c. 3. Suppose a, b, and c are integers such that alb. Then a|bc. 4. Suppose a, b, and c are integers such that alb and a|c. Then a|(b+c).
Transcribed Image Text:Prove or give a counterexample to the following statements. 1. Suppose a, b, and c are integers such that alc and b|c. Then a|b. 2. Suppose a, b, and c are integers such that alc and b|c. Then (a + b)|c. 3. Suppose a, b, and c are integers such that alb. Then a|bc. 4. Suppose a, b, and c are integers such that alb and a|c. Then a|(b+c).
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