Hello! can you please solve the problems? Write clearly and thank you! Prove or give a counterexample to the following statements.1. Suppose a, b, and c are integers such that alc and b|c. Thena|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. Thena|(b+c).

Answered: Image /qna-images/answer/7a6e1e3f-3800-4993-8de4-edb3a2c0e363.jpg

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).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 9TFE

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