Complete solutions of a family of quartic Thue and index form 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

按检索

Complete solutions of a family of quartic Thue and index form equations

Authors:	Maurice Mignotte Attila Pethö Ralf Roth

Institution:	Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France ; Department of Computer Science, Kossuth Lajos University, P.O. Box 12, H-4010 Debrecen, Hungary ; FB-14 Informatik, Universität des Saarlandes, Postfach 151150, D-66041 Saar- brücken, Germany

Abstract:	Continuing the recent work of the second author, we prove that the diophantine equation $\begin{displaymath}f_a(x,y)=x^4-ax^3 y-x^2 y^2+axy^3+y^4=1 \end{displaymath}$ for $\|a\|\ge 3$ has exactly 12 solutions except when , when it has 16 solutions. If $\alpha=\alpha(a)$ denotes one of the zeros of , then for $\|a\|\ge 4$ we also find all $\gamma\in\mathbb Z\alpha]$ with $\mathbb Z\gamma]=\mathbb Z\alpha]$ .

Keywords:	Thue equation index form equation linear forms in the logarithms of algebraic numbers distributed computation

	点击此处可从《Mathematics of Computation》浏览原始摘要信息
	点击此处可从《Mathematics of Computation》下载免费的PDF全文