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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the Diophantine equation $ x\sp 6\sb 1+x\sp 6\sb 2+x\sp 6\sb 3=y\sp 6\sb 1+y\sp 6\sb 2+y\sp 6\sb 3$

Author: Jean-Joël Delorme
Journal: Math. Comp. 59 (1992), 703-715
MSC: Primary 11D41; Secondary 11Y50
MathSciNet review: 1134725
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Abstract: In this paper, we develop an elementary method for producing parametric solutions of the equation $ x_1^6 + x_2^6 + x_3^6 = y_1^6 + y_2^6 + y_3^6$ by reducing the resolution of a system including it to that of the equation

\begin{displaymath}\begin{array}{*{20}{c}} {(s_1^2 + {{({s_1} + {t_1})}^2})(s_2^... ... + {t_2})}^2})(t_3^2 + {{({s_3} + {t_3})}^2}).} \\ \end{array} \end{displaymath}

We give such solutions of degrees 4, 5, 7, 8, 9, and 11.

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Article copyright: © Copyright 1992 American Mathematical Society