Geodesic
On some cubic equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 263-271.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper considers the structure of solutions of the system $$ \begin{cases} x_1+x_2+x_3=y_1+y_2+y_3 \\ x_1^3+x_2^3+x_3^3=y_1^3+y_2^3+y_3^3 \end{cases} $$ and the equation $$ x_1^3+x_2^3+x_3^3=y_1^3+y_2^3+y_3^3. $$ 
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A. V. Ustinov. On some cubic equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 263-271. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a18/

[1] Chondhry A., “Symmetric Dioph. Systems”, Acta Arith., 59 (1991), 291–307 | MR

[2] Dickson L. E., Introduction to the Theory of Numbers, Univ. of Chicago press, Chicago, 1931; Dikson L. E., Vvedenie v teoriyu chisel, Tbilisi, 1941