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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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