Rational solutions of cubic and quartic Diophantine equations
DOI :
https://doi.org/10.5269/bspm.77745Résumé
By employing an elementary approach, rational solutions of the Diophantine equations $x^3 + y^3 + z^3 =u^3 + v^3 + t^3$ and $x^4 + y^4 + z^4 =u^4 + v^4 + t^4$ are provided.
Références
Cabral, M.A.P, Marques, F.C. and Pombo Jr., D.P.,
Solutions of Diophantine equations in ordered fields,
J. Linear Topol. Algebra, 14(1), 15--36, (2025).
Marques, F.C. and Pombo Jr., D.P.,
Rational solutions of certain Diophantine equations,
JP J. Math. Sci., 31, 1--18, (2022).
Swinnerton-Dyer, P.,
A solution of $A^4+B^4=C^4+D^4$,
J. London Math. Soc., 18, 2--4, (1943).
Solutions of Diophantine equations in ordered fields,
J. Linear Topol. Algebra, 14(1), 15--36, (2025).
Marques, F.C. and Pombo Jr., D.P.,
Rational solutions of certain Diophantine equations,
JP J. Math. Sci., 31, 1--18, (2022).
Swinnerton-Dyer, P.,
A solution of $A^4+B^4=C^4+D^4$,
J. London Math. Soc., 18, 2--4, (1943).
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Publié
2026-06-05
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Research Articles
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© Boletim da Sociedade Paranaense de Matemática 2026
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