On two-parametric family of quartic Thue equations

Borka Jadrijević

doi:10.5802/jtnb.483

Borka Jadrijević ¹

¹ FESB, University of Split R. Boškovića bb 21000 Split, Croatia

Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 161-167.

Abstract
Résumé

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 $gcd (x y, m n) = 1$ .

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 $pgcd (x y, m n) = 1$ .

EuDML: 249420 | MR: 2152217 | Zbl: 1162.11327

DOI: 10.5802/jtnb.483

Author's affiliations:

Borka Jadrijević ¹

¹ FESB, University of Split R. Boškovića bb 21000 Split, Croatia

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Borka Jadrijević. On two-parametric family of quartic Thue equations. Journal de théorie des nombres de Bordeaux, Volume 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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