@preamble{"\providecommand{\noopsort}[1]{}"}

@misc{DahmenSiksek,
  author = {Dahmen, Sander R. and Siksek, Samir},
  title  = {On the generalized {F}ermat equation $x^5+y^3=z^7$},
  month  = {July},
  year   = {2024},
  note   = {Working paper, \url{https://few.vu.nl/~sdn249/GFE357.pdf}}
}

@manual{PARI,
  author  = {{\noopsort{PARI}The PARI~Group}},
  title   = {{PARI/GP} version 2.17.3},
  address = {Univ. Bordeaux},
  year    = {2025},
  note    = {\url{https://pari.math.u-bordeaux.fr/}}
}

@phdthesis{Putz,
  author = {Putz, Piet Hein Casper},
  title  = {Enumeration of local and global \'etale algebras applied to generalized {F}ermat equations},
  school = {Vrije Universiteit Amsterdam},
  year   = {2024},
  note   = {\url{https://doi.org/10.5463/thesis.832}}
}

@article{DarmonGranville,
  author  = {Darmon, Henri and Granville, Andrew},
  title   = {On the equations {$z^m=F(x,y)$} and {$Ax^p+By^q=Cz^r$}},
  journal = {Bull. Lond. Math. Soc.},
  volume  = {27},
  year    = {1995},
  number  = {6},
  pages   = {513--543},
  note    = {\url{https://doi.org/10.1112/blms/27.6.513}}
}

@incollection{BMS,
  author    = {Bennett, Michael A. and Mih\u{a}ilescu, Preda and Siksek, Samir},
  title     = {The generalized {F}ermat equation},
  booktitle = {Open problems in mathematics},
  editor    = {Nash, Jr., John Forbes and Rassias, Michael {\relax Th}.},
  publisher = {Springer, Cham},
  year      = {2016},
  pages     = {173--205},
  note      = {\url{https://doi.org/10.1007/978-3-319-32162-2_3}}
}

@article{Survey,
  author  = {Ratcliffe, Ashleigh and Grechuk, Bogdan},
  title   = {Generalized {F}ermat equation: a survey of solved cases},
  journal = {Expo. Math.},
  volume  = {43},
  year    = {2025},
  number  = {4},
  pages   = {Paper No. 125688},
  note    = {\url{https://doi.org/10.1016/j.exmath.2025.125688}; arXiv:2412.11933v2}
}

@article{PSS07,
  author  = {Poonen, Bjorn and Schaefer, Edward F. and Stoll, Michael},
  title   = {Twists of {$X(7)$} and primitive solutions to {\mbox{$x^2+y^3=z^7$}}},
  journal = {Duke Math. J.},
  volume  = {137},
  number  = {1},
  year    = {2007},
  pages   = {103--158},
  note    = {\url{https://doi.org/10.1215/S0012-7094-07-13714-1}}
}

@article{FNS20,
  author  = {Freitas, Nuno and Naskr{\k{e}}cki, Bartosz and Stoll, Michael},
  title   = {The generalized {F}ermat equation with exponents 2, 3, $n$},
  journal = {Compos. Math.},
  volume  = {156},
  number  = {1},
  year    = {2020},
  pages   = {77--113},
  note    = {\url{https://doi.org/10.1112/S0010437X19007693}}
}

@misc{Chocian26,
  author = {Chocian, Peter},
  title  = {The primitive generalized {F}ermat equation $x^3+y^5=z^7$: a computer-assisted proof},
  year   = {2026},
  note   = {Preprint, arXiv:2609.26996v1}
}

@manual{FLINT,
  author = {{\noopsort{FLINT}The FLINT team}},
  title  = {{FLINT}: {F}ast {L}ibrary for {N}umber {T}heory, version 3.3},
  year   = {2025},
  note   = {\url{https://flintlib.org}}
}

@misc{DahmenTalk,
  author = {Dahmen, Sander R.},
  title  = {Generalized {F}ermat equations with three distinct prime exponents},
  year   = {2025},
  note   = {Talk in the Number theory lunch seminar, Max Planck Institute for Mathematics, Bonn, 2 April 2025; abstract at \url{https://www.mpim-bonn.mpg.de/node/13952}}
}

@misc{Jaswal357,
  author = {Jaswal, Manvir},
  title  = {The generalized {F}ermat equation {$X^5+Y^3=Z^7$}},
  year   = {2026},
  note   = {Preprint, Zenodo, \url{https://doi.org/10.5281/zenodo.22949749}}
}

@misc{Companion257,
  author = {Jaswal, Manvir},
  title  = {Programs and data for ``{T}he generalized {F}ermat equation {$x^2+y^5=z^7$}''},
  year   = {2026},
  note   = {Zenodo, \url{https://doi.org/10.5281/zenodo.22983849}}
}

@misc{Lean257,
  author = {Jaswal, Manvir},
  title  = {Lean formalization: the generalized {F}ermat equation {$x^2+y^5=z^7$}},
  year   = {2026},
  note   = {Zenodo, \url{https://doi.org/10.5281/zenodo.23065698}}
}

@article{Weil52,
  author  = {Weil, Andr\'e},
  title   = {Sur les ``formules explicites'' de la th\'eorie des nombres premiers},
  journal = {Comm. S\'em. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.]},
  year    = {1952},
  volume  = {Tome suppl\'ementaire},
  pages   = {252--265}
}

@book{Lang,
  author    = {Lang, Serge},
  title     = {Algebraic number theory},
  edition   = {Second},
  series    = {Grad. Texts in Math.},
  volume    = {110},
  publisher = {Springer-Verlag, New York},
  year      = {1994}
}

@article{Poitou,
  author  = {Poitou, Georges},
  title   = {Sur les petits discriminants},
  journal = {S\'eminaire Delange--Pisot--Poitou. Th\'eorie des nombres},
  volume  = {18},
  number  = {1},
  year    = {1976/77},
  pages   = {Exp. No. 6, 1--17},
  note    = {\url{http://www.numdam.org/item/SDPP_1976-1977__18_1_A6_0/}}
}

@article{BDF08,
  author  = {Belabas, Karim and Diaz y Diaz, Francisco and Friedman, Eduardo},
  title   = {Small generators of the ideal class group},
  journal = {Math. Comp.},
  volume  = {77},
  year    = {2008},
  number  = {262},
  pages   = {1185--1197},
  note    = {\url{https://doi.org/10.1090/S0025-5718-07-02003-0}}
}

@article{Arb,
  author  = {Johansson, Fredrik},
  title   = {Arb: efficient arbitrary-precision midpoint-radius interval arithmetic},
  journal = {IEEE Trans. Comput.},
  volume  = {66},
  year    = {2017},
  number  = {8},
  pages   = {1281--1292},
  note    = {\url{https://doi.org/10.1109/TC.2017.2690633}}
}

@article{Darmon00,
  author  = {Darmon, Henri},
  title   = {Rigid local systems, {H}ilbert modular forms, and {F}ermat's last theorem},
  journal = {Duke Math. J.},
  volume  = {102},
  number  = {3},
  year    = {2000},
  pages   = {413--449},
  note    = {\url{https://doi.org/10.1215/S0012-7094-00-10233-5}}
}

@article{PS97,
  author  = {Poonen, Bjorn and Schaefer, Edward F.},
  title   = {Explicit descent for {J}acobians of cyclic covers of the projective line},
  journal = {J. Reine Angew. Math.},
  volume  = {488},
  year    = {1997},
  pages   = {141--188},
  note    = {\url{https://doi.org/10.1515/crll.1997.488.141}}
}

@article{BS09,
  author  = {Bruin, Nils and Stoll, Michael},
  title   = {Two-cover descent on hyperelliptic curves},
  journal = {Math. Comp.},
  volume  = {78},
  number  = {268},
  year    = {2009},
  pages   = {2347--2370},
  note    = {\url{https://doi.org/10.1090/S0025-5718-09-02255-8}}
}

@article{SS12,
  author  = {Siksek, Samir and Stoll, Michael},
  title   = {Partial descent on hyperelliptic curves and the generalized {F}ermat equation $x^3+y^4+z^5=0$},
  journal = {Bull. Lond. Math. Soc.},
  volume  = {44},
  number  = {1},
  year    = {2012},
  pages   = {151--166},
  note    = {\url{https://doi.org/10.1112/blms/bdr086}}
}

@misc{PutzEtale,
  author = {Putz, Piet Hein Casper},
  title  = {Families of \'etale algebras in {M}agma},
  year   = {2023},
  note   = {GitHub repository, commit 9481cf0 (22 January 2025), \url{https://github.com/CPutz/etale-algebra-family/tree/9481cf0}}
}

@misc{PutzHunter,
  author = {Putz, Piet Hein Casper},
  title  = {A parallel program for targeted {H}unter searches},
  year   = {2023},
  note   = {GitHub repository, commit 1c2e95d (22 January 2025), \url{https://github.com/CPutz/hunter_search/tree/1c2e95d}}
}

@misc{EV25,
  author = {Elsenhans, Andreas-Stephan and Voight, John},
  title  = {Computing class groups and unit groups in {M}agma},
  year   = {2025},
  note   = {Preprint, arXiv:2510.05501v1}
}