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The smallest solutions to the diophantine equation $x^6+y^6=a^6+b^6+c^6+d^6+e^6$

Authors: Giovanni Resta and Jean-Charles Meyrignac
Journal: Math. Comp. 72 (2003), 1051-1054
MSC (2000): Primary 11D41, 11Y50
Published electronically: June 6, 2002
MathSciNet review: 1954984
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Abstract: In this paper we discuss a method used to find the smallest nontrivial positive integer solutions to $a_1^6+a_2^6=b_1^6+b_2^6+b_3^6+b_4^6+b_5^6$. The method, which is an improvement over a simple brute force approach, can be applied to search the solution to similar equations involving sixth, eighth and tenth powers.

References [Enhancements On Off] (What's this?)

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  • 2. L.J. Lander, T.R. Parkin, J.L. Selfridge, A Survey of Equal Sums of Like Powers. Math. Comp. 21 (1967), 446-459. MR 36:5060
  • 3. B. Mazur, Questions about Powers of Numbers. Notices of the AMS, February 2000 195-202. MR 2000k:11111
  • 4. J.-C. Meyrignac, et al., Computing Minimal Equal Sums of Like Powers. Distributed computing project, see

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Additional Information

Giovanni Resta
Affiliation: Istituto di Matematica Computazionale -CNR, Pisa, Italy.

Jean-Charles Meyrignac

Keywords: Diophantine equations, computational number theory
Received by editor(s): May 24, 1999
Received by editor(s) in revised form: April 3, 2001, and July 9, 2001
Published electronically: June 6, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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