Computational investigations of the Prouhet-Tarry-Escott Problem
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- by Peter Borwein, Petr Lisoněk and Colin Percival;
- Math. Comp. 72 (2003), 2063-2070
- DOI: https://doi.org/10.1090/S0025-5718-02-01504-1
- Published electronically: December 18, 2002
Abstract:
We describe a method for searching for ideal symmetric solutions to the Prouhet-Tarry-Escott Problem. We report results of extensive searches for solutions of sizes up to 12. We found two solutions of size 10 that are smaller by two orders of magnitude than the solution found by A. Letac in the 1940s, which was the smallest size 10 solution known before our search.References
- P. Borwein, Excursions in Computational and Diophantine Number Theory. Springer-Verlag, New York (to appear).
- Peter Borwein and Colin Ingalls, The Prouhet-Tarry-Escott problem revisited, Enseign. Math. (2) 40 (1994), no. 1-2, 3–27. MR 1279058
- Andrew Bremner, A geometric approach to equal sums of fifth powers, J. Number Theory 13 (1981), no. 3, 337–354. MR 634204, DOI 10.1016/0022-314X(81)90019-6
- Chen Shuwen, The Prouhet-Tarry-Escott Problem. http://member.netease.com/~chin/eslp/TarryPrb.htm
- A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8
- Elmer Rees and Christopher Smyth, On the constant in the Tarry-Escott problem, Cinquante ans de polynômes (Paris, 1988) Lecture Notes in Math., vol. 1415, Springer, Berlin, 1990, pp. 196–208. MR 1044114, DOI 10.1007/BFb0084888
Bibliographic Information
- Peter Borwein
- Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada
- Email: pborwein@cecm.sfu.ca
- Petr Lisoněk
- Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada
- Email: lisonek@cecm.sfu.ca
- Colin Percival
- Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada
- Address at time of publication: Wadham College, Oxford University, Oxford, England
- Email: cperciva@sfu.ca
- Received by editor(s): November 9, 2001
- Received by editor(s) in revised form: March 25, 2002
- Published electronically: December 18, 2002
- Additional Notes: Research presented in this paper was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and partially by the National Centre of Excellence MITACS
- © Copyright 2002 by the authors
- Journal: Math. Comp. 72 (2003), 2063-2070
- MSC (2000): Primary 11D72, 11Y50; Secondary 11P05
- DOI: https://doi.org/10.1090/S0025-5718-02-01504-1
- MathSciNet review: 1986822