Computers & Mathematics with ApplicationsVolume 61, Issue 9, May 2011, Pages 2914-2923Solutions of a class of quartic Thue inequalitiesAuthor links open overlay panelBo He a, Omar Kihel b, Alain Togbé cShow moreShareCitehttps://doi.org/10.1016/j.camwa.2011.03.080Get rights and contentUnder an Elsevier user licenseopen archiveAbstractLet n>1 be an integer. In this paper, first we show that the quartic Thue equality x4−(n+1)x3y−nx2y2+2xy3+y4=μ can be transformed into a system of Pellian equations by the Tzanakis method if and only if n=c2+c−5, for some integer c≥3. We determine all positive integer solutions (x,y) with 0<∣μ∣≤c+2.Previous article in issueNext article in issueKeywordsThue inequalitiesMethod of TzanakisContinued fractionsRecommended articlesCited by (0)Copyright © 2011 Elsevier Ltd. All rights reserved.