Classical and Modular Approaches to Exponential Diophantine Equations Ii. the Lebesgue–nagell Equation
نویسندگان
چکیده
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 x +D = y, x, y integers, n ≥ 3, for D in the range 1 ≤ D ≤ 100.
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