Cassels’ Relations

Yuri F. Bilu, Yann Bugeaud and Maurice Mignotte
Additional contact information
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 3 in The Problem of Catalan, 2014, pp 27-35 from Springer

Abstract: Abstract Due to the results of the previous chapter, we may assume that the exponents of Catalan’s equation are odd and consider the equation x p − y q = 1 $$x^{p} - y^{q} = 1$$ in nonzero integers x, y and odd primes p, q. In this chapter we prove Cassels’ divisibility theorem: p∣y and q∣x. This allows one to reduce the initial equation to several more complicated equations (“Cassels’ relations”), which are, however, easier to deal with. We also show, following Hyyrö, that Cassels’ relations imply lower bounds for | x | (and | y | ) in terms of p and q.

Keywords: Divisibility Theorem; Complicated Equations; Nonzero Integer; Lower Bound; Initial Equations (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10094-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319100944

DOI: 10.1007/978-3-319-10094-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().