English

Computing rational solutions to $Ax^p+By^p+Cz^p=0$

Number Theory 2025-05-16 v1

Abstract

In this survey, we studied the possibility of finding rational solutions to the equation Axp+Byp+Czp=0Ax^p+By^p+Cz^p=0 via its attached hyperelliptic curve Y2=Xp+A2(BC)p1/4Y^2=X^p+A^2(BC)^{p-1}/4 and its rational points computed using computational tools.

Cite

@article{arxiv.2505.09641,
  title  = {Computing rational solutions to $Ax^p+By^p+Cz^p=0$},
  author = {Alejandro Argáez-García},
  journal= {arXiv preprint arXiv:2505.09641},
  year   = {2025}
}
R2 v1 2026-06-28T23:33:28.548Z