On the Diophantine equation 𝑥⁶₁+𝑥⁶₂+𝑥⁶₃=𝑦⁶₁+𝑦⁶₂+𝑦⁶₃

Delorme, Jean-Joël

doi:10.1090/S0025-5718-1992-1134725-3

On the Diophantine equation $x^ 6_ 1+x^ 6_ 2+x^ 6_ 3=y^ 6_ 1+y^ 6_ 2+y^ 6_ 3$
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by Jean-Joël Delorme PDF

Math. Comp. 59 (1992), 703-715 Request permission

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 \[ \begin {array}{*{20}{c}} {(s_1^2 + {{({s_1} + {t_1})}^2})(s_2^2 + {{({s_2} + {t_2})}^2})(s_3^2 + {{({s_3} + {t_3})}^2})} \\ { = (t_1^2 + {{({s_1} + {t_1})}^2})(t_2^2 + {{({s_2} + {t_2})}^2})(t_3^2 + {{({s_3} + {t_3})}^2}).} \\ \end {array} \] We give such solutions of degrees 4, 5, 7, 8, 9, and 11.

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On sums of sixth powers

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