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

2004/05/12 by Yann Bugeaud, Maurice Mignotte, Bugeaud, Yann +3 · 1 citation
Mathematics · #11D59 #11D61 #11J86 #11Y50 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D59 #msc:11D61 #msc:11J86 #msc:11Y50

paper · pdf · doi:10.48550/arxiv.math/0405220

49 pages

arxiv created 2004/05/12 · arxiv updated 2009/12/01

Abstract

We solve completely the Lebesgue-Nagell equation x²+D=yⁿ, in integers x, y, n>2, for D in the range 1 =< D =< 100.

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