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Search for good examples of Hall's conjecture


Authors: Stål Aanderaa, Lars Kristiansen and Hans Kristian Ruud
Journal: Math. Comp. 87 (2018), 2903-2914
MSC (2010): Primary 11Y50, 65A05; Secondary 11D25
DOI: https://doi.org/10.1090/mcom/3298
Published electronically: January 18, 2018
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Abstract: A good example of Hall's conjecture is a pair of natural numbers $ x,y$ such that $ 0 < \vert x^3 - y^2\vert < x^{1/2}$. We have implemented a new algorithm and found nine not previously known good examples. Moreover, we have verified that all good examples with $ x < 10^{29}$ are now found.


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Additional Information

Stål Aanderaa
Affiliation: Department of Mathematics University of Oslo P.O. Box 1053 Blindern NO-0316 Oslo Norway
Email: staal@math.uio.no

Lars Kristiansen
Affiliation: Department of Mathematics University of Oslo P.O. Box 1053 Blindern NO-0316 Oslo Norway
Email: larsk@math.uio.no

Hans Kristian Ruud
Affiliation: Department of Mathematics University of Oslo P.O. Box 1053 Blindern NO-0316 Oslo Norway

DOI: https://doi.org/10.1090/mcom/3298
Received by editor(s): November 15, 2015
Received by editor(s) in revised form: November 16, 2016, and May 17, 2017
Published electronically: January 18, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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