A conjecture on a symmetric diagonal Diophantine equation of degree six

Azar Jalali, Ali S Janfada, Hassan Shabani-Solt

Abstract


It is conjectured that the symmetric diagonal Diophantine equation $x^6+ky^3+k'z^3=u^6+kv^3+k'w^3$ has infinitely many nontrivial solutions for all rational numbers $k$ and $k'$. This conjecture is proved for certain cases.

Keywords


Counting solutions of Diophantine equations, elliptic curves

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