Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation

[摘要] This is the second in a series of papers where we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last Theorem. In this paper we use a general and powerful new lower bound for linear forms in three logarithms, together with a combination of classical, elementary and substantially improved modular methods to solve completely the Lebesgue–Nagell equation x2 + D = yn, x, y integers, $ngeq 3$, for D in the range $1 leq D leq 100$.

[学科分类] 数学（综合）