The Number of Solutions of Certain Equations over Finite Fields

Let s be a positive integer, p be an odd prime, [see formula in PDF], and let [see formula in PDF] be a finite field of q elements. Let [see formula in PDF] be the number of solutions of the following equations: [see formula in PDF][see formula in PDF] over the finite field [see formula in PDF], wit...

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Bibliographic Details
Published inWuhan University journal of natural sciences Vol. 27; no. 1; pp. 49 - 52
Main Authors HU, Shuangnian, LIU, Jianghan, QIN, Zhentao
Format Journal Article
LanguageEnglish
Published 01.03.2022
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Summary:Let s be a positive integer, p be an odd prime, [see formula in PDF], and let [see formula in PDF] be a finite field of q elements. Let [see formula in PDF] be the number of solutions of the following equations: [see formula in PDF][see formula in PDF] over the finite field [see formula in PDF], with [see formula in PDF][see formula in PDF][see formula in PDF] and [see formula in PDF][see formula in PDF] are positive integers. In this paper, we find formulas for [see formula in PDF] when there is a positive integer l such that dD |([see formula in PDF]) , where [see formula in PDF][see formula in PDF][see formula in PDF][see formula in PDF][see formula in PDF][see formula in PDF][see formula in PDF][see formula in PDF] And we determine [see formula in PDF] explicitly under certain cases. This extends Markoff-Hurwitz-type equations over finite field.
ISSN:1007-1202
1993-4998
DOI:10.1051/wujns/2022271049