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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

New results in equal sums of like powers


Author: Randy L. Ekl
Journal: Math. Comp. 67 (1998), 1309-1315
MSC (1991): Primary 11D41; Secondary 11Y50
MathSciNet review: 1474650
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Abstract: This paper reports on new results for the equation

\begin{equation*}\sum _{i=1}^{m} a_{i}^{k}=\sum _{j=1}^{n} b_{j}^{k},\end{equation*}

i.e., equal sums of like powers. Since the 1967 Lander, Parkin and Selfridge survey paper [4], few other numeric results have been published (see Elkies [6] and Ekl [3]). The present paper reports on several new smallest primitive solutions. Further, search limits have been extended in many cases, and tables of solutions are presented. Additionally, new solutions to the same class of problems in distinct integers have been discovered.


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Additional Information

Randy L. Ekl
Affiliation: 930 Lancaster Lane, Lake Zurich, IL 60047
Email: randye@comm.mot.com

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00979-X
PII: S 0025-5718(98)00979-X
Keywords: Number theory, diophantine equation, computational number theory, Euler's conjecture
Received by editor(s): September 30, 1996
Article copyright: © Copyright 1998 American Mathematical Society