PILLAI'S CONJECTURE FOR POLYNOMIALS

被引：0

作者：

Heintze, Sebastian ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Anal & Number Theory, Steyrergasse 30-II, A-8010 Graz, Austria

来源：

GLASNIK MATEMATICKI | 2023年 / 58卷 / 01期

基金：

奥地利科学基金会;

关键词：

Pillai problem; polynomials; units;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation p(n) - q(m) = f. We prove that for any non-constant polynomial f there are only finitely many quadruples (n, m, deg p, deg q) consisting of integers n, m >= 2 and non-constant polynomials p, q such that Pillai's equation holds. Moreover, we will give some examples that there can still be infinitely many possibilities for the polynomials p, q.

引用

页码：67 / 74

页数：8

共 8 条

[1] On some exponential equations of S. S. Pillai [J].

Bennett, MA .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2001, 53 (05) :897-922

[2] VANISHING SUMS IN FUNCTION-FIELDS [J].

BROWNAWELL, WD ;

MASSER, DW .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1986, 100 :427-434

[3] On a variant of Pillai's problem II [J].

Chim, Kwok Chi ;

Pink, Istvan ;

Ziegler, Volker .

JOURNAL OF NUMBER THEORY, 2018, 183 :269-290

[4] A function field variant of Pillai's problem [J].

Fuchs, Clemens ;

Heintze, Sebastian .

JOURNAL OF NUMBER THEORY, 2021, 222 :278-292

[5] Decomposable polynomials in second order linear recurrence sequences [J].

Fuchs, Clemens ;

Karolus, Christina ;

Kreso, Dijana .

MANUSCRIPTA MATHEMATICA, 2019, 159 (3-4) :321-346

[6]

Kreso D., PREPRINTS

[7]

Mihailescu P, 2004, J REINE ANGEW MATH, V572, P167

[8]

Pillai SS., 1936, J. Indian Math. Soc. (NS), V2, P119

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