On x-coordinates of pell equations that are repdigits

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901Y18" target="_blank" >RIV/61988987:17310/18:A1901Y18 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On x-coordinates of pell equations that are repdigits

Original language description

Let b ? 2 be a given integer. In this paper, we show that there are only finitely many positive integers d that are not squares, such that the Pell equation X2 ? dY 2 = 1 has two positive integer solutions (X, Y) with the property that their X-coordinates are base b-repdigits. Recall that a base b-repdigit is a positive integer whose digits have the same value when written in base b. We also give an upper bound on the largest such d in terms of b.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

FIBONACCI QUART

ISSN

0015-0517

e-ISSN

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Volume of the periodical

56

Issue of the periodical within the volume

1

Country of publishing house

CA - CANADA

Number of pages

11

Pages from-to

52-62

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85043677191