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Let a, b, and e be integers, where a # 0. Then (i) if alb and alc, then al(b + c); (ii) if alb, then al bc for all integers c; (iii) if alb and blc, then alc.

Let a, b, and e be integers, where a # 0. Then (i) if alb and alc, then al(b + c); (ii) if alb, then al bc for all integers c; (iii) if alb and blc, then alc.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 21E: Prove that if and are integers such that and , then either or .
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Prove that part (iii) of Theorem 1 is true.

THEOREM 1 Let a, b, and e be integers, where a # 0. Then (i) if alb and alc, then al(b + c); (ii) if alb, then al bc for all integers c; (iii) if alb and blc, then alc.
Transcribed Image Text:THEOREM 1 Let a, b, and e be integers, where a # 0. Then (i) if alb and alc, then al(b + c); (ii) if alb, then al bc for all integers c; (iii) if alb and blc, then alc.
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