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Akinari Hoshi
Complete solutions to a family of Thue equations of degree 12
Journal de théorie des nombres de Bordeaux, 29 no. 2 (2017), p. 549-568, doi: 10.5802/jtnb.991
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Class. Math.: 11D25, 11D41, 11R16, 11R20, 12F10
Keywords: Thue equations, simplest cubic fields, simplest sextic fields.

Résumé - Abstract

We consider a parametric non-Galois family of Thue equations $F_m(x,y)=\lambda$ of degree $12$ where $m$ is an integral parameter and $\lambda$ is a divisor of $729(m^2+3m+9)$. Using the field isomorphism method which is developed in [15], we show that the equations have only the trivial solutions with $xy(x+y)(x-y)(x+2y)(2x+y)=0$.

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