% BibTeX database for Long solutions to small equations.

@book{ATLAS85,
  author    = {Conway, J. H. and Curtis, R. T. and Norton, S. P. and Parker, R. A. and Wilson, R. A.},
  title     = {Atlas of Finite Groups},
  publisher = {Oxford University Press},
  address   = {Oxford},
  year      = {1985}
}

@article{BB12,
  author  = {Balakrishnan, Jennifer S. and Besser, Amnon},
  title   = {Computing local p-adic height pairings on hyperelliptic curves},
  journal = {International Mathematics Research Notices. IMRN},
  year    = {2012},
  number  = {11},
  pages   = {2405--2444},
  eprint  = {1010.6009},
  archivePrefix = {arXiv}
}

@article{BB15,
  author  = {Balakrishnan, Jennifer S. and Besser, Amnon},
  title   = {Coleman--{G}ross height pairings and the p-adic sigma function},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {698},
  year    = {2015},
  pages   = {89--104},
  eprint  = {1201.6016},
  archivePrefix = {arXiv}
}

@article{BBM16,
  author  = {Balakrishnan, Jennifer S. and Besser, Amnon and M{\"u}ller, J. Steffen},
  title   = {Quadratic {C}habauty: p-adic heights and integral points on hyperelliptic curves},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {720},
  year    = {2016},
  pages   = {51--79},
  doi     = {10.1515/crelle-2014-0048},
  eprint  = {1302.2944},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1515/crelle-2014-0048}}
}

@article{BCDT01,
  author  = {Breuil, Christophe and Conrad, Brian and Diamond, Fred and Taylor, Richard},
  title   = {On the modularity of elliptic curves over {$\mathbf{Q}$}: wild 3-adic exercises},
  journal = {Journal of the American Mathematical Society},
  volume  = {14},
  number  = {4},
  year    = {2001},
  pages   = {843--939},
  doi     = {10.1090/S0894-0347-01-00370-8},
  note = {\url{https://doi.org/10.1090/S0894-0347-01-00370-8}}
}

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

@article{BEN10,
  author = {Bennett, Michael A. and Ellenberg, Jordan S. and Ng, Nathan C.},
  title = {The {Diophantine} equation {$A^4+2^\delta B^2=C^n$}},
  journal = {International Journal of Number Theory},
  volume = {6},
  number = {2},
  pages = {311--338},
  year = {2010},
  doi = {10.1142/S1793042110002971},
  note = {\url{https://doi.org/10.1142/S1793042110002971}}
}

@book{BLR90,
  author    = {Bosch, Siegfried and L{\"u}tkebohmert, Werner and Raynaud, Michel},
  title     = {N{\'e}ron Models},
  series    = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3)},
  volume    = {21},
  publisher = {Springer-Verlag},
  address   = {Berlin},
  year      = {1990},
  doi       = {10.1007/978-3-642-51438-8},
  note = {\url{https://doi.org/10.1007/978-3-642-51438-8}}
}

@article{BPS16,
  author  = {Bruin, Nils and Poonen, Bjorn and Stoll, Michael},
  title   = {Generalized explicit descent and its application to curves of genus 3},
  journal = {Forum of Mathematics, Sigma},
  volume  = {4},
  year    = {2016},
  pages   = {e6},
  doi     = {10.1017/fms.2016.1},
  eprint  = {1205.4456},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1017/fms.2016.1}}
}

@article{Brown12,
  author = {Brown, David},
  title = {Primitive integral solutions to {$x^2+y^3=z^{10}$}},
  journal = {International Mathematics Research Notices},
  volume = {2012},
  number = {2},
  pages = {423--436},
  year = {2012},
  doi = {10.1093/imrn/rnr022},
  note = {\url{https://doi.org/10.1093/imrn/rnr022}}
}

@article{Bruin03,
  author  = {Bruin, Nils},
  title   = {Chabauty methods using elliptic curves},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {562},
  year    = {2003},
  pages   = {27--49}
}

@article{Bruin08,
  author  = {Bruin, Nils},
  title   = {The arithmetic of {P}rym varieties in genus 3},
  journal = {Compositio Mathematica},
  volume  = {144},
  year    = {2008},
  pages   = {317--338},
  doi     = {10.1112/S0010437X07003314},
  eprint  = {math/0408069},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1112/S0010437X07003314}}
}

@article{BS09,
  author  = {Bruin, Nils and Stoll, Michael},
  title   = {Two-cover descent on hyperelliptic curves},
  journal = {Mathematics of Computation},
  volume  = {78},
  number  = {268},
  year    = {2009},
  pages   = {2347--2370},
  doi     = {10.1090/S0025-5718-09-02255-8},
  eprint  = {0803.2052},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1090/S0025-5718-09-02255-8}}
}

@article{BS10,
  author  = {Bruin, Nils and Stoll, Michael},
  title   = {The {M}ordell--{W}eil sieve: proving non-existence of rational points on curves},
  journal = {LMS Journal of Computation and Mathematics},
  volume  = {13},
  year    = {2010},
  pages   = {272--306},
  doi     = {10.1112/S1461157009000187},
  eprint  = {0906.1934},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1112/S1461157009000187}}
}

@article{BVY04,
  author = {Bennett, Michael A. and Vatsal, Vinayak and Yazdani, Soroosh},
  title = {Ternary {Diophantine} equations of signature {$(p,p,3)$}},
  journal = {Compositio Mathematica},
  volume = {140},
  number = {6},
  pages = {1399--1416},
  year = {2004},
  doi = {10.1112/S0010437X04000983},
  note = {\url{https://doi.org/10.1112/S0010437X04000983}}
}

@book{CF96,
  author    = {Cassels, J. W. S. and Flynn, E. V.},
  title     = {Prolegomena to a middlebrow arithmetic of curves of genus 2},
  series    = {London Mathematical Society Lecture Note Series},
  volume    = {230},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1996}
}

@incollection{CG89,
  author    = {Coleman, Robert F. and Gross, Benedict H.},
  title     = {p-adic heights on curves},
  booktitle = {Algebraic number theory -- in honor of K. Iwasawa},
  series    = {Advanced Studies in Pure Mathematics},
  volume    = {17},
  publisher = {Academic Press},
  address   = {Boston, MA},
  year      = {1989},
  pages     = {73--81}
}

@book{Cohen93,
  author    = {Cohen, Henri},
  title     = {A Course in Computational Algebraic Number Theory},
  series    = {Graduate Texts in Mathematics},
  volume    = {138},
  publisher = {Springer-Verlag},
  address   = {Berlin},
  year      = {1993}
}

@article{Coleman85,
  author  = {Coleman, Robert F.},
  title   = {Effective {C}habauty},
  journal = {Duke Mathematical Journal},
  volume  = {52},
  number  = {3},
  year    = {1985},
  pages   = {765--770},
  doi     = {10.1215/S0012-7094-85-05240-8},
  note = {\url{https://doi.org/10.1215/S0012-7094-85-05240-8}}
}

@book{CTS21, author={Colliot-Th\'el\`ene, Jean-Louis and Skorobogatov, Alexei N.}, title={The {B}rauer--{G}rothendieck Group}, series={Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge}, volume={71}, publisher={Springer}, address={Cham}, year={2021}}

@article{DG95,
  author  = {Darmon, Henri and Granville, Andrew},
  title   = {On the equations $z^m=F(x,y)$ and $Ax^p+By^q=Cz^r$},
  journal = {Bulletin of the London Mathematical Society},
  volume  = {27},
  number  = {6},
  year    = {1995},
  pages   = {513--543},
  doi     = {10.1112/blms/27.6.513},
  note = {\url{https://doi.org/10.1112/blms/27.6.513}}
}

@book{Dolgachev12,
  author    = {Dolgachev, Igor V.},
  title     = {Classical Algebraic Geometry: A Modern View},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2012}
}

@misc{Dusart10,
  author  = {Dusart, Pierre},
  title   = {Estimates of some functions over primes without {R.H.}},
  year    = {2010},
  eprint  = {1002.0442},
  archivePrefix = {arXiv}
}

@article{EJ12, author={Elsenhans, Andreas-Stephan and Jahnel, J\"org}, title={On the order three {B}rauer classes for cubic surfaces}, journal={Central European Journal of Mathematics}, volume={10}, number={3}, year={2012}, pages={903--926}, doi={10.2478/s11533-012-0042-6}, note={arXiv:1110.2086. \url{https://doi.org/10.2478/s11533-012-0042-6}}}

@article{FW99,
  author  = {Flynn, E. V. and Wetherell, J. L.},
  title   = {Finding rational points on bielliptic genus 2 curves},
  journal = {Manuscripta Mathematica},
  volume  = {100},
  number  = {4},
  year    = {1999},
  pages   = {519--533}
}

@article{GH81,
  author  = {Gross, Benedict H. and Harris, Joe},
  title   = {Real algebraic curves},
  journal = {Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure (4)},
  volume  = {14},
  number  = {2},
  year    = {1981},
  pages   = {157--182},
  doi     = {10.24033/asens.1401},
  note = {\url{https://doi.org/10.24033/asens.1401}}
}

@book{Grechuk24,
  author    = {Grechuk, Bogdan},
  title     = {Polynomial {D}iophantine Equations: A Systematic Approach},
  publisher = {Springer},
  address   = {Cham},
  year      = {2024},
  doi       = {10.1007/978-3-031-62949-5},
  note = {\url{https://doi.org/10.1007/978-3-031-62949-5}}
}

@misc{GrechukMO26,
  author = {Grechuk, Bogdan},
  title = {Answer to ``What are the primitive solutions to {$x^3+2y^3=z^4$}?''},
  year = {2026},
  howpublished = {MathOverflow, question 484736},
  note = {Answer dated 10 July 2026; includes the reduction for exponent 5. \url{https://mathoverflow.net/questions/484736/}}
}

@misc{GrechukOpen,
  author = {Grechuk, Bogdan},
  title = {A systematic approach to {Diophantine} equations: open problems},
  year = {2026},
  eprint = {2404.08518},
  archivePrefix = {arXiv},
  note = {Available at \url{https://arxiv.org/abs/2404.08518}}
}

@incollection{Gross86,
  author    = {Gross, Benedict H.},
  title     = {Local heights on curves},
  booktitle = {Arithmetic Geometry ({S}torrs, {C}onn., 1984)},
  editor    = {Cornell, Gary and Silverman, Joseph H.},
  publisher = {Springer},
  address   = {New York},
  year      = {1986},
  pages     = {327--339}
}

@book{Hartshorne77,
  author    = {Hartshorne, Robin},
  title     = {Algebraic Geometry},
  series    = {Graduate Texts in Mathematics},
  volume    = {52},
  publisher = {Springer-Verlag},
  address   = {New York},
  year      = {1977}
}

@book{Hazewinkel78,
  author    = {Hazewinkel, Michiel},
  title     = {Formal Groups and Applications},
  series    = {Pure and Applied Mathematics},
  volume    = {78},
  publisher = {Academic Press},
  address   = {New York},
  year      = {1978}
}

@article{Katz81,
  author  = {Katz, Nicholas M.},
  title   = {Galois properties of torsion points on abelian varieties},
  journal = {Inventiones Mathematicae},
  volume  = {62},
  number  = {3},
  year    = {1981},
  pages   = {481--502},
  doi     = {10.1007/BF01394256},
  note = {\url{https://doi.org/10.1007/BF01394256}}
}

@article{KRZB16,
  author  = {Katz, Eric and Rabinoff, Joseph and Zureick-Brown, David},
  title   = {Uniform bounds for the number of rational points on curves of small {M}ordell--{W}eil rank},
  journal = {Duke Mathematical Journal},
  volume  = {165},
  number  = {16},
  year    = {2016},
  pages   = {3189--3240},
  doi     = {10.1215/00127094-3673558},
  eprint  = {1504.00694},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1215/00127094-3673558}}
}

@article{Lemmermeyer13,
  author  = {Lemmermeyer, Franz},
  title   = {The ambiguous class number formula revisited},
  journal = {Journal of the Ramanujan Mathematical Society},
  volume  = {28},
  number  = {4},
  year    = {2013},
  pages   = {415--421},
  eprint  = {1309.1071},
  archivePrefix = {arXiv}
}

@book{Matsumura86, author={Matsumura, Hideyuki}, title={Commutative Ring Theory}, series={Cambridge Studies in Advanced Mathematics}, volume={8}, publisher={Cambridge University Press}, address={Cambridge}, year={1986}, note={Translated from the Japanese by M. Reid}}

@article{Mazur77,
  author  = {Mazur, Barry},
  title   = {Modular curves and the {E}isenstein ideal},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume  = {47},
  year    = {1977},
  pages   = {33--186},
  doi     = {10.1007/BF02684339},
  note = {\url{https://doi.org/10.1007/BF02684339}}
}

@article{Mihailescu04,
  author = {Mih{\u a}ilescu, Preda},
  title = {Primary cyclotomic units and a proof of {Catalan}'s conjecture},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume = {572},
  pages = {167--195},
  year = {2004},
  doi = {10.1515/crll.2004.048},
  note = {\url{https://doi.org/10.1515/crll.2004.048}}
}

@article{Miller14,
  author  = {Miller, John C.},
  title   = {Class numbers of totally real fields and applications to the {W}eber class number problem},
  journal = {Acta Arithmetica},
  volume  = {164},
  number  = {4},
  year    = {2014},
  pages   = {381--397},
  doi     = {10.4064/aa164-4-4},
  eprint  = {1405.1094},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.4064/aa164-4-4}}
}

@incollection{MP12,
  author    = {McCallum, William and Poonen, Bjorn},
  title     = {The method of {C}habauty and {C}oleman},
  booktitle = {Explicit methods in number theory: rational points and Diophantine equations},
  series    = {Panoramas et Synth{\`e}ses},
  volume    = {36},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  address   = {Paris},
  year      = {2012},
  pages     = {99--117}
}

@book{Neukirch99, author={Neukirch, J{\"u}rgen}, title={Algebraic Number Theory}, series={Grundlehren der mathematischen Wissenschaften}, volume={322}, publisher={Springer-Verlag}, address={Berlin}, year={1999}}

@article{OT70,
  author  = {Tate, John and Oort, Frans},
  title   = {Group schemes of prime order},
  journal = {Annales Scientifiques de l'{\'E}cole Normale Sup{\'e}rieure (4)},
  volume  = {3},
  year    = {1970},
  pages   = {1--21}
}

@article{Poitou77,
  author  = {Poitou, Georges},
  title   = {Sur les petits discriminants},
  journal = {S{\'e}minaire Delange--Pisot--Poitou, Th{\'e}orie des nombres},
  volume  = {18},
  number  = {1},
  year    = {1976/77},
  pages   = {1--17},
  note    = {Expos{\'e} no.~6}
}

@book{Poonen17, author={Poonen, Bjorn}, title={Rational Points on Varieties}, series={Graduate Studies in Mathematics}, volume={186}, publisher={American Mathematical Society}, address={Providence, RI}, year={2017}}

@article{PS97,
  author  = {Poonen, Bjorn and Schaefer, Edward F.},
  title   = {Explicit descent for {J}acobians of cyclic covers of the projective line},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {488},
  year    = {1997},
  pages   = {141--188}
}

@article{PS99,
  author  = {Poonen, Bjorn and Stoll, Michael},
  title   = {The {C}assels--{T}ate pairing on polarized abelian varieties},
  journal = {Annals of Mathematics (2)},
  volume  = {150},
  number  = {3},
  year    = {1999},
  pages   = {1109--1149},
  doi     = {10.2307/121064},
  eprint  = {math/9911267},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.2307/121064}}
}

@article{Raynaud74,
  author  = {Raynaud, Michel},
  title   = {Sch{\'e}mas en groupes de type $(p,\dots,p)$},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume  = {102},
  year    = {1974},
  pages   = {241--280}
}

@article{RG25,
  author = {Ratcliffe, Ashleigh and Grechuk, Bogdan},
  title = {Generalised {Fermat} equation: a survey of solved cases},
  journal = {Expositiones Mathematicae},
  volume = {43},
  number = {4},
  pages = {125688},
  year = {2025},
  doi = {10.1016/j.exmath.2025.125688},
  eprint = {2412.11933v2},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1016/j.exmath.2025.125688}}
}

@article{RR18,
  author  = {Ritzenthaler, Christophe and Romagny, Matthieu},
  title   = {On the {P}rym variety of genus 3 covers of genus 1 curves},
  journal = {{\'E}pijournal de G{\'e}om{\'e}trie Alg{\'e}brique},
  volume  = {2},
  year    = {2018},
  pages   = {Article No.~2},
  doi     = {10.46298/epiga.2018.volume2.3663},
  eprint  = {1612.07033},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.46298/epiga.2018.volume2.3663}}
}

@article{Schaefer98,
  author  = {Schaefer, Edward F.},
  title   = {Computing a {S}elmer group of a {J}acobian using functions on the curve},
  journal = {Mathematische Annalen},
  volume  = {310},
  number  = {3},
  year    = {1998},
  pages   = {447--471}
}

@book{Serre73, author={Serre, Jean-Pierre}, title={A Course in Arithmetic}, series={Graduate Texts in Mathematics}, volume={7}, publisher={Springer-Verlag}, address={New York}, year={1973}}

@article{Serre87,
  author  = {Serre, Jean-Pierre},
  title   = {Sur les repr{\'e}sentations modulaires de degr{\'e} 2 de {$\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})$}},
  journal = {Duke Mathematical Journal},
  volume  = {54},
  number  = {1},
  year    = {1987},
  pages   = {179--230},
  doi     = {10.1215/S0012-7094-87-05413-5},
  note = {\url{https://doi.org/10.1215/S0012-7094-87-05413-5}}
}

@book{Serre88,
  author    = {Serre, Jean-Pierre},
  title     = {Algebraic Groups and Class Fields},
  series    = {Graduate Texts in Mathematics},
  volume    = {117},
  publisher = {Springer-Verlag},
  address   = {New York},
  year      = {1988}
}

@incollection{Sik12,
  author    = {Siksek, Samir},
  title     = {The modular approach to {D}iophantine equations},
  booktitle = {Explicit Methods in Number Theory: Rational Points and {D}iophantine Equations},
  series    = {Panoramas et Synth{\`e}ses},
  volume    = {36},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  address   = {Paris},
  year      = {2012},
  pages     = {151--179}
}

@book{Silverman09,
  author    = {Silverman, Joseph H.},
  title     = {The Arithmetic of Elliptic Curves},
  edition   = {Second},
  series    = {Graduate Texts in Mathematics},
  volume    = {106},
  publisher = {Springer},
  address   = {New York},
  year      = {2009},
  doi       = {10.1007/978-0-387-09494-6},
  note = {\url{https://doi.org/10.1007/978-0-387-09494-6}}
}

@book{Silverman94,
  author    = {Silverman, Joseph H.},
  title     = {Advanced Topics in the Arithmetic of Elliptic Curves},
  series    = {Graduate Texts in Mathematics},
  volume    = {151},
  publisher = {Springer},
  address   = {New York},
  year      = {1994},
  doi       = {10.1007/978-1-4612-0851-8},
  note = {\url{https://doi.org/10.1007/978-1-4612-0851-8}}
}

@article{Simon02,
  author  = {Simon, Denis},
  title   = {Computing the rank of elliptic curves over number fields},
  journal = {LMS Journal of Computation and Mathematics},
  volume  = {5},
  year    = {2002},
  pages   = {7--17},
  doi     = {10.1112/S1461157000000668},
  note = {\url{https://doi.org/10.1112/S1461157000000668}}
}

@article{Stoll01,
  author  = {Stoll, Michael},
  title   = {Implementing 2-descent for {J}acobians of hyperelliptic curves},
  journal = {Acta Arithmetica},
  volume  = {98},
  number  = {3},
  year    = {2001},
  pages   = {245--277},
  doi     = {10.4064/aa98-3-4},
  note = {\url{https://doi.org/10.4064/aa98-3-4}}
}

@article{Stoll02,
  author  = {Stoll, Michael},
  title   = {On the height constant for curves of genus two, {II}},
  journal = {Acta Arithmetica},
  volume  = {104},
  number  = {2},
  year    = {2002},
  pages   = {165--182},
  doi     = {10.4064/aa104-2-6},
  note = {\url{https://doi.org/10.4064/aa104-2-6}}
}

@article{Stoll99,
  author  = {Stoll, Michael},
  title   = {On the height constant for curves of genus two},
  journal = {Acta Arithmetica},
  volume  = {90},
  number  = {2},
  year    = {1999},
  pages   = {183--201},
  doi     = {10.4064/aa-90-2-183-201},
  note = {\url{https://doi.org/10.4064/aa-90-2-183-201}}
}

@article{Strassmann28,
  author  = {Stra{\ss}mann, Reinhold},
  title   = {{\"U}ber den {W}ertevorrat von {P}otenzreihen im {G}ebiet der p-adischen {Z}ahlen},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {159},
  year    = {1928},
  pages   = {13--28},
  doi     = {10.1515/crll.1928.159.13},
  note = {\url{https://doi.org/10.1515/crll.1928.159.13}}
}

@incollection{Sturm87,
  author    = {Sturm, Jacob},
  title     = {On the congruence of modular forms},
  booktitle = {Number Theory (New York, 1984--1985)},
  series    = {Lecture Notes in Mathematics},
  volume    = {1240},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1987},
  pages     = {275--280}
}

@incollection{Tate75,
  author    = {Tate, John},
  title     = {Algorithm for determining the type of a singular fiber in an elliptic pencil},
  booktitle = {Modular Functions of One Variable {IV} (Antwerp, 1972)},
  series    = {Lecture Notes in Mathematics},
  volume    = {476},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1975},
  pages     = {33--52}
}

@article{TW95,
  author  = {Taylor, Richard and Wiles, Andrew},
  title   = {Ring-theoretic properties of certain {H}ecke algebras},
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  volume  = {141},
  number  = {3},
  year    = {1995},
  pages   = {553--572},
  doi     = {10.2307/2118560},
  note = {\url{https://doi.org/10.2307/2118560}}
}

@book{Weil48,
  author    = {Weil, Andr{\'e}},
  title     = {Sur les courbes alg{\'e}briques et les vari{\'e}t{\'e}s qui s'en d{\'e}duisent},
  series    = {Actualit{\'e}s Sci. Ind., no. 1041 = Publ. Inst. Math. Univ. Strasbourg 7 (1945)},
  publisher = {Hermann et Cie.},
  address   = {Paris},
  year      = {1948}
}

@article{Weil52,
  author  = {Weil, Andr{\'e}},
  title   = {Sur les ``formules explicites'' de la th{\'e}orie des nombres premiers},
  journal = {Comm. S{\'e}m. Math. Univ. Lund},
  year    = {1952},
  pages   = {252--265},
  note    = {Volume d{\'e}di{\'e} {\`a} Marcel Riesz; {\OE}uvres scientifiques II, 48--61}
}

@misc{Wilcox24,
  author = {Wilcox, Ashleigh},
  title = {A systematic approach to {Diophantine} equations: two thousand solved examples},
  year = {2024},
  eprint = {2404.08719v2},
  archivePrefix = {arXiv},
  howpublished = {\url{https://arxiv.org/abs/2404.08719v2}},
  note = {Version 2, 17 December 2024; Appendix A was added in this revision}
}

@article{Wiles95,
  author  = {Wiles, Andrew},
  title   = {Modular elliptic curves and {F}ermat's {L}ast {T}heorem},
  journal = {Annals of Mathematics (2)},
  volume  = {141},
  number  = {3},
  year    = {1995},
  pages   = {443--551},
  doi     = {10.2307/2118559},
  note = {\url{https://doi.org/10.2307/2118559}}
}

@article{ZhangBai14,
  author = {Zhang, Zhongfeng and Bai, Meng},
  title = {On {Diophantine} equation {$x^3+y^3=2z^{2n}$}},
  journal = {Journal of Southwest China Normal University (Natural Science Edition)},
  volume = {39},
  number = {6},
  pages = {14--16},
  year = {2014},
  doi = {10.13718/j.cnki.xsxb.2014.06.004},
  note = {In Chinese. \url{https://doi.org/10.13718/j.cnki.xsxb.2014.06.004}}
}

@misc{grechuk2026certifying,
  title = {Certifying non-existence of integer points on curves},
  author = {Grechuk, Bogdan and Go, Eugene},
  year = {2026},
  howpublished = {arXiv:2610.18916},
  note = {\url{https://arxiv.org/abs/2610.18916}}
}

@article{grechuk2026cubic,
	author={Grechuk, Bogdan},
	title={Cubic {Diophantine} equations: integer solutions beyond direct search},
	journal={The American Mathematical Monthly}, year={2026}, note={To appear}
}
@article{grechuk2026shortest,
	author={Grechuk, Bogdan and Ratcliffe, Ashleigh},
	title={On the shortest open cubic equations},
	journal={International Journal of Number Theory},
	volume={22}, number={9}, pages={2117--2127}, year={2026},
	note={\url{https://doi.org/10.1142/S1793042126501058}}
}
@misc{grechuk2026polynomial,
	author={Grechuk, Bogdan and Agbanwa, Jamal},
	title={On the polynomial values represented by {binary} quadratic forms},
	year={2026}, note={arXiv:2607.06627, \url{https://arxiv.org/abs/2607.06627}}
}

% Earlier Hexagon papers.
@misc{hexagon:2609.00132v1,
  title = {Primitive Integer Solutions of {$x^4+3y^3+2z^3=0$}},
  author = {Eisenberg, Avraham},
  howpublished = {Hexagon preprint 2609.00132v1},
  year = {2026},
  month = sep,
  note = {Version 1, 29 September 2026. \url{https://hexagonmath.org/2609.00132v1}},
  url = {https://hexagonmath.org/2609.00132v1}
}

@misc{hexagon:2609.00130v1,
  title = {Primitive Integer Solutions of {$x^4+4y^3+z^3=0$}},
  author = {Eisenberg, Avraham},
  howpublished = {Hexagon preprint 2609.00130v1},
  year = {2026},
  month = sep,
  note = {Version 1, 29 September 2026. \url{https://hexagonmath.org/2609.00130v1}},
  url = {https://hexagonmath.org/2609.00130v1}
}