A conjecture on a symmetric diagonal Diophantine equation of degree six

Authors

  • Azar Jalali
  • Ali S Janfada Urmia University
  • Hassan Shabani-Solt

Keywords:

Counting solutions of Diophantine equations, elliptic curves

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.

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Published

2020-12-27

Issue

Vol. 15

Section

Vol. 15, No. 4, (2021)

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