Abstract. We use the hypergeometric method to solve three families of Thue inequalities of degree 3, 4 and 6, respectively, each of which is parametrized by an integral parameter. We obtain bounds for the solutions, which are astonishingly small compared to similar results which use estimates of linear forms in logarithms.

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We will give a new version of proof for Furtwängler's characterization of all ideals of an algebraic number field which appear as conductors of orders of the field.Mathematics Subject Classification (2010). Primary 11R04; Secondary 13F05.