Search for good examples of Hall’s conjecture
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- by Stål Aanderaa, Lars Kristiansen and Hans Kristian Ruud PDF
- Math. Comp. 87 (2018), 2903-2914 Request permission
Abstract:
A good example of Hall’s conjecture is a pair of natural numbers $x,y$ such that $0 < |x^3 - y^2| < x^{1/2}$. 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.References
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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
- MR Author ID: 617768
- Email: larsk@math.uio.no
- Hans Kristian Ruud
- Affiliation: Department of Mathematics,University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo,Norway
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 2903-2914
- MSC (2010): Primary 11Y50, 65A05; Secondary 11D25
- DOI: https://doi.org/10.1090/mcom/3298
- MathSciNet review: 3834691