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On equal sums of ninth powers

Author(s): A. Bremner; Jean-Joël Delorme.
Journal: Math. Comp. 79 (2010), 603-612.
MSC (2000): Primary 11D41, 11G05
Posted: July 8, 2009
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Abstract: In this paper, we develop an elementary method to obtain infinitely many solutions of the Diophantine equation

$\displaystyle x_{1}^9+x_{2}^9+x_{3}^9+x_{4}^9+x_{5}^9+x_{6}^9=y_{1}^9+y_{2}^9+y_{3}^9+y_{4}^9+y_{5}^9+y_{6}^9 $

and we give some numerical results.

References:

1.
R. EKL, New results in equal sums of like powers, Math. Comp. 67, no. 223 (1998), 1309-1315. MR 1474650 (98m:11023)

2.
L.J. LANDER, T.R. PARKIN, AND J.L. SELFRIDGE, A survey of equal sums of like powers, Math. Comp. 21 (1967), 446-459. MR 0222008 (36:5060)

3.
W. BOSMA, J. CANNON, AND C. PLAYOUST, The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4): 235-265, 1997. MR 1484478

4.
A. MOESSNER, On Equal Sums of Like Powers, Math. Student 15 (1947), 83-88. MR 0033840 (11:500a)

5.
TITUS PIEZAS III, Timeline of Euler's Extended Conjecture, http://www.geocities.com/titus_piezas/Timeline1.htm.

6.
T. SHIODA, On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972) 20-59. MR 0429918 (55:2927)

7.
E.W. WEISSTEIN, Diophantine Equation-9th Powers, http://mathworld.wolfram.com/DiophantineEquation9thPowers.html

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Additional Information:

A. Bremner
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona
Email: bremner@asu.edu

Jean-Joël Delorme
Affiliation: 6 rue des émeraudes, 69006 Lyon, France
Email: jean.joel.delorme@wanadoo.fr

DOI: 10.1090/S0025-5718-09-02288-1
PII: S 0025-5718(09)02288-1
Received by editor(s): March 3, 2009
Posted: July 8, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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