A parametric family of quintic Thue equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A parametric family of quintic Thue equations

Authors:	Istvá n Gaá l Gü nter Lettl.

Affiliation:	Kossuth Lajos University, Mathematical Institute, H--4010 Debrecen Pf.12., Hungary ; Karl-Franzens-Universität Graz, Institut für Mathematik, A--8010 Graz, Heinrichstraße 36, Austria

Abstract:	For an integral parameter we investigate the family of Thue equations $begin{multline}F(x,y) = x^{5} + (t-1)^{2}x^{4}y - (2t^{3}+4t+4)x^{3}y^{2} + (t^{4}+t^{3}+2t^{2}+4t-3)x^{2}y^{3} + (t^{3}+t^{2}+5t+3)xy^{4} + y^{5} = pm 1,, end{multline}$ originating from Emma Lehmer's family of quintic fields, and show that for $\|t\| ge 3.28 cdot 10^{15}$ the only solutions are the trivial ones with or . Our arguments contain some new ideas in comparison with the standard methods for Thue families, which gives this family a special interest.

Keywords:	Parametric Thue equation Baker's method

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