The extension of some D(4)-pairs

Alan Filipin
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 126–135
Full paper (PDF, 189 Kb)

Details

Authors and affiliations

Alan Filipin
Faculty of Civil Engineering, University of Zagreb
Fra Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia

Abstract

In this paper we illustrate the use of the results from [1] proving that D(4)-triple {a,b,c} with a < b < a+57√ a  has a unique extension to a quadruple with a larger element. This furthermore implies that D(4)-pair {a,b} cannot be extended to a a quintuple if a < b < a+57√ a .

Keywords

• Diophantine m-tuples
• Simultaneous Diophantine equations

AMS Classification

• Primary 11D09
• Secondary 11J68

References

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