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

DOI:
https://doi.org/10.1090/S0025-5718-98-00979-X

MathSciNet review:
1474650

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper reports on new results for the 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.

**1.**Guy, Richard K.,*Unsolved Problems in Number Theory, Second Edition*, Springer-Verlag, Ney York, 1994. MR**96e:11002****2.**Hardy, G.H. and Wright, E. M.,*Introduction to the Theory of Numbers, 5th edition*, Oxford University Press, New York, 1980. MR**81i:10002****3.**Ekl, Randy L.,*Equal Sums of Four Seventh Powers*, Mathematics of Computation**65**(1996), 1755-1756. MR**97a:11050****4.**Lander, L. J., Parkin, T. R. and Selfridge, J. L.,*A Survey of Equal Sums of Like Powers*, Mathematics of Computation**21**(1967), 446-459. MR**36:5060****5.**Letac, A., Gazeta Matematica**48**(1942), 66-69.**6.**Elkies, Noam,*On*, Mathematics of Computation**51**(1988), 825-835. MR**89h:11012****7.**Scher, Bob and Seidl, Ed,*Seven Sevens*, personal correspondence (Sept. 19, 1996).**8.**Subba Rao, K.,*On sums of sixth powers*, J. London Math. Soc.**9**(1934), 172-173.**9.**Moessner, A.,*Einige numerische Identitaten*, Proc. Indian Acad. Sci. Sect. A**10**(1939), 296-306.**10.**Dickson, L. E.,*History of the Theory of Numbers, Vol. II*, Addison-Wesley, London, 1956. MR**39:6807e**

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Additional Information

**Randy L. Ekl**

Affiliation:
930 Lancaster Lane, Lake Zurich, IL 60047

Email:
randye@comm.mot.com

DOI:
https://doi.org/10.1090/S0025-5718-98-00979-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