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Let p be a prime number and let Z∗ p = {1,2,...,p −1}, then show that 1. Z∗p is closed under ·p, 2. ·p has an identity element in Z∗p, 3. every element in Z∗p has a ·p-inverse in Z∗p (hint: for any x ∈ Z∗ p we have gcd(x,p) = 1).

Let p be a prime number and let Z∗ p = {1,2,...,p −1}, then show that 1. Z∗p is closed under ·p, 2. ·p has an identity element in Z∗p, 3. every element in Z∗p has a ·p-inverse in Z∗p (hint: for any x ∈ Z∗ p we have gcd(x,p) = 1).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 3E: 3. Let be an integral domain with positive characteristic. Prove that all nonzero elements of...
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Let p be a prime number and let Z∗
 p = {1,2,...,p −1}, then show
 that
 1. Z∗p is closed under ·p,
 2. ·p has an identity element in Z∗p,
 3. every element in Z∗p has a ·p-inverse in Z∗p (hint: for any x ∈ Z∗
 p we have gcd(x,p) = 1).

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