On Y-coordinates of Pell equations which are Lucas numbers

被引：1

作者：

Edjeou, Bilizimbeye ^{[1
]}

Faye, Bernadette ^{[2
]}

Gomez, Carlos A. ^{[3
]}

Luca, Florian ^{[4
,5
,6
,7
]}

机构：

[1] Univ Gaston Berger, Ecole Doctorale Sci & Technol, St Louis 234, Senegal

[2] Univ Gaston Berger, UFR SAT, St Louis 234, Senegal

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

[4] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

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

[6] Max Planck Inst Software Syst, Saarbrucken, Germany

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

来源：

RAMANUJAN JOURNAL | 2022年 / 59卷 / 04期

关键词：

Diophantine equations; Lucas sequence; Pell equation; LOGARITHMS; FORMS;

D O I：

10.1007/s11139-022-00613-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d >= 2 be an integer which is not a square. We show that if (L-n)(n >= 0) is the Lucas sequence and (X-m, Y-m)(m >= 1) is the mth solution of the Pell equation X-2 - dY(2) = +/- 1, then the equation Y-m = L-n has at most two positive integer solutions (m, n) except for d = 2 when it has the three solutions (m, n) = (1, 1), (2, 0), (5, 7).

引用

页码：1091 / 1136

页数：46

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