Arithmetic progressions on Pell equations

A. Pethő, V. Ziegler

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X, Y) whose X-coordinates or Y-coordinates are in arithmetic progression.

Original languageEnglish
Pages (from-to)1389-1409
Number of pages21
JournalJournal of Number Theory
Volume128
Issue number6
DOIs
Publication statusPublished - Jun 2008

Fingerprint

Pell's equation
Arithmetic sequence
Integral Solution

Keywords

  • Arithmetic progressions
  • Elliptic curves
  • Pell equations

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Arithmetic progressions on Pell equations. / Pethő, A.; Ziegler, V.

In: Journal of Number Theory, Vol. 128, No. 6, 06.2008, p. 1389-1409.

Research output: Contribution to journalArticle

Pethő, A. ; Ziegler, V. / Arithmetic progressions on Pell equations. In: Journal of Number Theory. 2008 ; Vol. 128, No. 6. pp. 1389-1409.
@article{6edd7a54e5154fc1be625322c394d713,
title = "Arithmetic progressions on Pell equations",
abstract = "In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X, Y) whose X-coordinates or Y-coordinates are in arithmetic progression.",
keywords = "Arithmetic progressions, Elliptic curves, Pell equations",
author = "A. Pethő and V. Ziegler",
year = "2008",
month = "6",
doi = "10.1016/j.jnt.2008.01.003",
language = "English",
volume = "128",
pages = "1389--1409",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "6",

}

TY - JOUR

T1 - Arithmetic progressions on Pell equations

AU - Pethő, A.

AU - Ziegler, V.

PY - 2008/6

Y1 - 2008/6

N2 - In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X, Y) whose X-coordinates or Y-coordinates are in arithmetic progression.

AB - In this paper we consider arithmetic progressions on Pell equations, i.e. integral solutions (X, Y) whose X-coordinates or Y-coordinates are in arithmetic progression.

KW - Arithmetic progressions

KW - Elliptic curves

KW - Pell equations

UR - http://www.scopus.com/inward/record.url?scp=43049084408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049084408&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2008.01.003

DO - 10.1016/j.jnt.2008.01.003

M3 - Article

AN - SCOPUS:43049084408

VL - 128

SP - 1389

EP - 1409

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 6

ER -