Open Access
April 2009 Rational Diophantine sextuples with mixed signs
Andrej Dujella
Proc. Japan Acad. Ser. A Math. Sci. 85(4): 27-30 (April 2009). DOI: 10.3792/pjaa.85.27

Abstract

A rational Diophantine $m$-tuple is a set of $m$ nonzero rationals such that the product of any two of them is one less than a perfect square. Recently Gibbs constructed several examples of rational Diophantine sextuples with positive elements. In this note, we construct examples of rational Diophantine sextuples with mixed signs. Indeed, we show that such examples exist for all possible combinations of signs.

Citation

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Andrej Dujella. "Rational Diophantine sextuples with mixed signs." Proc. Japan Acad. Ser. A Math. Sci. 85 (4) 27 - 30, April 2009. https://doi.org/10.3792/pjaa.85.27

Information

Published: April 2009
First available in Project Euclid: 2 April 2009

zbMATH: 1213.11066
MathSciNet: MR2517291
Digital Object Identifier: 10.3792/pjaa.85.27

Subjects:
Primary: 11D09 , 11G05 , 11Y50

Keywords: Diophantine sextuples , Elliptic curve

Rights: Copyright © 2009 The Japan Academy

Vol.85 • No. 4 • April 2009
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