Answered: Suppose that F is a field of order 125…

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Suppose that F is a field of order 125 and F* = <α>. Show thatα62 = -1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 12E

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Question

Suppose that F is a field of order 125 and F* = <α>. Show that
α⁶² = -1.

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