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Thue equations Ghadermarzi, Amir

Abstract

In this dissertation, we are mainly interested in effective methods to solve parametrized Thue equations. After briefly talking about the different effective methods, two parametrized families of cubic Thue equations are completely solved by using Pad é approximation and linear forms in logarithms. The Thue inequality ∣x³ + pxy² + qy³ ∣≤ k, is studied by using Bombieri's method. We find all solutions under some conditions on k, p and q. As an application of Thue equations, we find the integral points on the Mordell curves Y² = X³ + k for all nonzero integers k with ∣k∣ ≤ 10⁷ . Our approach uses a classical connection between these equations and cubic Thue equations.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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