any positive integer n, let Z∗n denote the set of all elements in Zn that are not zero factors. An element a ∈ Zn is a zero factor if there exists a nonzero element b ∈ Zm such that ab = 0 in Zn. For example in Z15 10 is a zero-factor because 10 × 3 = 30 = 0 in Z15. Compute Z∗ 30.

any positive integer n, let Z∗n denote the set of all elements in Zn that are not zero factors. An element a ∈ Zn is a zero factor if there exists a nonzero element b ∈ Zm such that ab = 0 in Zn. For example in Z15 10 is a zero-factor because 10 × 3 = 30 = 0 in Z15. Compute Z∗ 30.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.6: Congruence Classes

Problem 26E: Prove that a nonzero element in is a zero divisor if and only if and are not relatively prime.

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Question

or any positive integer n, let Z∗n denote the set of all elements in Zn that are not zero factors. An element a ∈ Zn is a zero factor if there exists a nonzero element b ∈ Zm such that ab = 0 in Zn. For example in Z15 10 is a zero-factor because 10 × 3 = 30 = 0 in Z15. Compute Z∗ 30.

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