Remarks on existentially closed fields and diophantine equations
Rendiconti del Seminario Matematico della Università di Padova, Volume 71  (1984), p. 229-237
@article{RSMUP_1984__71__229_0,
     author = {Ribenboim, Paulo},
     title = {Remarks on existentially closed fields and diophantine equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {71},
     year = {1984},
     pages = {229-237},
     zbl = {0545.12012},
     mrnumber = {769439},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1984__71__229_0}
}
Ribenboim, Paulo. Remarks on existentially closed fields and diophantine equations. Rendiconti del Seminario Matematico della Università di Padova, Volume 71 (1984) , pp. 229-237. http://www.numdam.org/item/RSMUP_1984__71__229_0/

[1] L. Van Den Dries, Model Theory of Fields, Decidability and Bounds for Polynomial Ideals, Thesis, University of Utrecht, 1978.

[2] N. Greenleaf, On Fermat's equation in C(t), Amer. Math. Monthly, 76 (1969), pp. 808-809. | MR 250973 | Zbl 0191.04905

[3] R. Liouville, Sur l'impossibilité de la relation algébriqne Xn + Yn + Zn = 0, C. R. Acad. Sci. Paris, 87 (1879), pp. 1108-1110. | JFM 11.0138.03

[4] M. Natanson, Catalan's equation in k(t), Amer. Math. Monthly, 81 (1974), pp. 371-373. | MR 335436 | Zbl 0282.10008

[5] P. Ribenboim, Théorie des Valuation, Presses Université de Montréal, 1964. | MR 249425 | Zbl 0139.26201

[6] P. Ribenboim, On the completion of a valuation ring, Math. Annalen, 155 (1964), pp. 392-396. | MR 164960 | Zbl 0136.32102