On two-parametric family of quartic Thue equations

Jadrijević, Borka

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

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

$$x^4-2mn{x}^{3}y+2\left(m^2-n^2+1\right)x^2{y}^2+2mnx{y}^3+y^4=1,$$

satisfaisant la condition supplémentaire $\text{pgcd}(xy,mn)=1$.

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

$$x^4-2mn{x}^{3}y+2\left(m^2-n^2+1\right)x^2{y}^2+2mnx{y}^3+y^4=1,$$

satisfying the additional condition $gcd(xy,mn)=1$.

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