On two-parametric family of quartic Thue equations

Borka Jadrijević

doi:10.5802/jtnb.483

Borka Jadrijević

Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 161-167.

Résumé
Abstract

Nous montrons que pour tous les entiers $m$ et $n$ , il n’y a pas de solution non triviale de l’équation de Thue

x^{4} - 2 m n x^{3} y + 2 (m^{2} - n^{2} + 1) x^{2} y^{2} + 2 m n x y^{3} + y^{4} = 1,

satisfaisant la condition supplémentaire $pgcd (x y, m n) = 1$ .

We show that for all integers $m$ and $n$ there are no non-trivial solutions of Thue equation

x^{4} - 2 m n x^{3} y + 2 (m^{2} - n^{2} + 1) x^{2} y^{2} + 2 m n x y^{3} + y^{4} = 1,

satisfying the additional condition $gcd (x y, m n) = 1$ .

Publié le : 2008-12-02

MR 2152217 | Zbl 1162.11327

DOI : https://doi.org/10.5802/jtnb.483

@article{JTNB_2005__17_1_161_0,
     author = {Borka Jadrijevi\'c},
     title = {On two-parametric family of quartic {Thue} equations},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {161--167},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {1},
     year = {2005},
     doi = {10.5802/jtnb.483},
     zbl = {1162.11327},
     mrnumber = {2152217},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.483/}
}

Borka Jadrijević. On two-parametric family of quartic Thue equations. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 161-167. doi : 10.5802/jtnb.483. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.483/

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