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Computational investigations of the Prouhet-Tarry-Escott Problem
Author(s):
Peter
Borwein;
Petr
Lisonek;
Colin
Percival.
Journal:
Math. Comp.
72
(2003),
2063-2070.
MSC (2000):
Primary 11D72, 11Y50;
Secondary 11P05
Posted:
December 18, 2002
MathSciNet review:
1986822
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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:
-
- 1.
- P. Borwein, Excursions in Computational and Diophantine Number Theory. Springer-Verlag, New York (to appear).
- 2.
- P. Borwein, C. Ingalls, The Prouhet-Tarry-Escott Problem revisited. Enseign. Math. 40 (1994), 3-27. MR 95d:11038
- 3.
- A. Bremner, A geometric approach to equal sums of fifth powers. J. Number Theory 13 (1981), no. 3, 337-354. MR 83g:14017
- 4.
- Chen Shuwen, The Prouhet-Tarry-Escott Problem. http://member.netease.com/~chin/eslp/TarryPrb.htm
- 5.
- A. Gloden, Mehrgradige Gleichungen. Second Edition. P. Noordhoff, Groningen, 1944. MR 8:441f
- 6.
- E. Rees, C. Smyth, On the constant in the Tarry-Escott Problem. Cinquante ans de polynômes (Paris, 1988), 196-208, Lecture Notes in Math., 1415, Springer, Berlin, 1990. MR 91g:11030
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Additional Information:
Peter
Borwein
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada
Email:
pborwein@cecm.sfu.ca
Petr
Lisonek
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
DOI:
10.1090/S0025-5718-02-01504-1
PII:
S 0025-5718(02)01504-1
Received by editor(s):
November 9, 2001
Received by editor(s) in revised form:
March 25, 2002
Posted:
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 of article:
Copyright
2002,
by the authors
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