Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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
MathSciNet review: 2552243
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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:

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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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