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AN UPPER BOUND FOR THE NUMBER OF DIOPHANTINE QUINTUPLES

Part of: Diophantine equations Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  16 August 2016

MARIJA BLIZNAC  and
ALAN FILIPIN
MARIJA BLIZNAC*
Affiliation:
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia email marija.bliznac@grad.hr
ALAN FILIPIN
Affiliation:
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia email filipin@grad.hr
*
✉marija.bliznac@grad.hr
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Abstract

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We improve the known upper bound for the number of Diophantine $D(4)$-quintuples by using the most recent methods that were developed in the $D(1)$ case. More precisely, we prove that there are at most $6.8587\times 10^{29}$$D(4)$-quintuples.

Keywords

Diophantine m-tuplesPell equations

MSC classification

Primary: 11D09: Quadratic and bilinear equations
Secondary: 11D45: Counting solutions of Diophantine equations 11J86: Linear forms in logarithms; Baker's method
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 384 - 394
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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