Primitive Integral Solutions to x² + y³ = z¹⁰

2009/11/16 by Brown, David · 1 citation
#11D41 #11G18 #11G30 #14G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0911.2932

Abstract

We classify primitive integer solutions to x² + y³ = z¹0. The technique is to combine modular methods at the prime 5, number field enumeration techniques in place of modular methods at the prime 2, Chabauty techniques for elliptic curves over number fields, and local methods.

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• The inter-universal Teichmüller theory and new Diophantine results over rational numbers. II

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