Higher Divisibility Theorems

Yuri F. Bilu, Yann Bugeaud and Maurice Mignotte
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Yuri F. Bilu: University of Bordeaux and CNRS, Institute of Mathematics of Bordeaux
Yann Bugeaud: University of Strasbourg and CNRS, IRMA, Mathematical Institute
Maurice Mignotte: University of Strasbourg and CNRS, IRMA, Mathematical Institute

Chapter Chapter 6 in The Problem of Catalan, 2014, pp 65-73 from Springer

Abstract: Abstract In this chapter we give first applications of the theory of cyclotomic fields to Catalan’s problem. We drastically refine Cassels’ divisibility theorem, showing that p 2∣y (and q 2∣x by symmetry). First we do this under an additional restriction (Inkeri) and then unconditionally (Mihăilescu).

Keywords: Prime Ideal; Class Group; Galois Group; Group Ring; Class Number (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10094-4_6

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DOI: 10.1007/978-3-319-10094-4_6

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