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Find the smallest field of characteristic 2 that contains an elementwhose multiplicative order is 5 and the smallest field of characteristic3 that contains an element whose multiplicative order is 5.

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 18E

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Find the smallest field of characteristic 2 that contains an element
whose multiplicative order is 5 and the smallest field of characteristic
3 that contains an element whose multiplicative order is 5.

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