On the x-coordinates of Pell equations which are rep-digits

被引：23

作者：

Dossavi-Yovo, Appolinaire ^{[1
]}

Luca, Florian ^{[2
]}

Togbe, Alain ^{[3
]}

机构：

[1] Inst Math & Sci Phys, Porto Novo, Benin

[2] Univ Witwatersrand, Sch Math, Private Bag X3, ZA-2050 Johannesburg, South Africa

[3] Purdue Univ, Dept Math, North Cent 1401 S,US 421, Westville, IN 46391 USA

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2016年 / 88卷 / 3-4期

关键词：

Pell equation; rep-digit; linear forms in complex and p-adic logarithms; FIBONACCI; REPDIGITS; SEQUENCES; NUMBERS;

D O I：

10.5486/PMD.2016.7378

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a positive integer d which is not a square, we show that there is at most one value of the positive integer x participating in the Pell equation x(2) - dy(2) = 1 which is a rep-digit, that is all its base 10 digits are equal, with a few exceptions in the pairs (d, x) which we determine.

引用

页码：381 / 399

页数：19

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