The diophantine equation aX 4 - BY 2 = 1

Shabnam Akhtari

doi:10.1515/CRELLE.2009.034

The diophantine equation aX ⁴ - BY ² = 1

Shabnam Akhtari

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX ⁴ - bY ² = 1, for fixed positive integers a and b, possesses at most two solutions in positive integers X and Y. Since there are infinitely many pairs (a, b) for which two such solutions exist, this result is sharp.

Original language	English (US)
Pages (from-to)	33-57
Number of pages	25
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	630
DOIs	https://doi.org/10.1515/CRELLE.2009.034
State	Published - May 2009

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2009.034

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abstract = "As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX 4 - bY 2 = 1, for fixed positive integers a and b, possesses at most two solutions in positive integers X and Y. Since there are infinitely many pairs (a, b) for which two such solutions exist, this result is sharp.",

author = "Shabnam Akhtari",

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AB - As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX 4 - bY 2 = 1, for fixed positive integers a and b, possesses at most two solutions in positive integers X and Y. Since there are infinitely many pairs (a, b) for which two such solutions exist, this result is sharp.

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The diophantine equation aX ⁴ - BY ² = 1

Abstract

All Science Journal Classification (ASJC) codes

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