JOURNAL ARTICLE
有限域中非零元表为两本原元和的问题
Year: 1990 Journal: Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese) Vol: 20 (11)Pages: 1146-1153 Publisher: Science China Press
Abstract
对Golomb的猜想:“存在正整数q0,使当素数幂q>q0时,有限域GF(q)中任一非零元皆可表为其两个本原元之和”,已有人给出了这样的q0,但相当大.本文的目的在于对任意素数幂q=pn,考察是否GF(q)中任一非零元皆可表为该域的两个本原元之和.我们证明了,对以下情形之一,这个答案是肯定的:(1)q>6.62×107,且q≠300690391,(2)n>1,且q≠22.而在q<10500的范围内,全部的否定答案仅是q=2,3,4,5,7,11,13,19,31,43,61这11个阶数.
Keywords:
Physics
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Topics
Rings, Modules, and Algebras
Physical Sciences → Mathematics → Algebra and Number Theory
Analytic Number Theory Research
Physical Sciences → Mathematics → Algebra and Number Theory
Finite Group Theory Research
Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics
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