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A new algorithm to search for small nonzero $ \vert x^3-y^2\vert$ values


Authors: I. Jiménez Calvo, J. Herranz and G. Sáez
Journal: Math. Comp. 78 (2009), 2435-2444
MSC (2000): Primary 11Y50, 65A05; Secondary 11D25, 14H52
Published electronically: February 13, 2009
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Abstract: In relation to Hall's conjecture, a new algorithm is presented to search for small nonzero $ k=\lvert x^3-y^2\rvert$ values. Seventeen new values of $ k<x^{1/2}$ are reported.


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Additional Information

I. Jiménez Calvo
Affiliation: C/Virgen de las Viñas 11, 28031–Madrid, Spain
Email: ijcalvo@gmail.com

J. Herranz
Affiliation: IIIA-CSIC, Campus de la UAB, E-08193 Bellaterra, Catalonia, Spain
Email: jherranz@iiia.csic.es

G. Sáez
Affiliation: Dept. de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, c/Jordi Girona, 1-3, 08034-Barcelona, Spain
Email: german@ma4.upc.es

DOI: https://doi.org/10.1090/S0025-5718-09-02240-6
Keywords: Hall's conjecture, Mordell's equation
Received by editor(s): April 18, 2005
Received by editor(s) in revised form: November 11, 2008
Published electronically: February 13, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.