Let p E Z be a prime number and set Zp = {- e Q : If gcd(n, m) = 1, then p m}. a. Show that Zp 1 Q.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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Let p E Z be a prime number and set Zp = {- eQ: If gcd(n, m) = 1, then p {m.
a. Show that Zp 1 Q.
Transcribed Image Text:Let p E Z be a prime number and set Zp = {- eQ: If gcd(n, m) = 1, then p {m. a. Show that Zp 1 Q.
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