Elliptic curves over finite fields with Fibonacci numbers of points

被引：0

作者：

Bilu, Yuri ^{[1
,2
]}

Gomez, Carlos A. ^{[3
]}

Gomez, Jhonny C. ^{[3
]}

Luca, Florian ^{[4
,5
,6
]}

机构：

[1] Univ Bordeaux, IMB, 351 Cours Liberat, F-33405 Talence, France

[2] CNRS, 351 Cours Liberat, F-33405 Talence, France

[3] Univ Valle, Dept Matemat, Calle 13 100-00, Cali 25360, Colombia

[4] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[5] King Abdulaziz Univ, Res Grp Algebra Struct & Applicat, Jeddah, Saudi Arabia

[6] UNAM, Ctr Ciencias Matemat, Morelia, Michoacan, Mexico

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2020年 / 26卷

关键词：

Fibonacci numbers; elliptic curves; linear forms in logarithms; Baker-Davenport reduction; LOGARITHMS; THEOREM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a prime power q and an elliptic curve E over F-q having q +1- a points, where a is an element of [-2 root q, 2 root q] let {#E-m}, m >= 1 be the sequence of numbers whose mth term is the number of points of E over F-q(m). In this paper, we determine all instances when #({#E-m}(m >= 1) boolean AND {F-n}(n >= 1)) >= 2, where {F-n}(n >= 1) is the sequence of Fibonacci numbers. That is, we determine all six-tuples (a, q, m(1), m(2), n(1), n(2)) such that #E = q +1- a, #E-m1 = F-n1 and #E-m2 = F-n2.

引用

页码：711 / 734

页数：24

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