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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Published in | Wuhan University journal of natural sciences Vol. 27; no. 1; pp. 49 - 52 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
01.03.2022
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Online Access | Get full text |
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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. |
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ISSN: | 1007-1202 1993-4998 |
DOI: | 10.1051/wujns/2022271049 |