Alternative Orderings of Diophantine Equations

Bogdan Grechuk
Additional contact information
Bogdan Grechuk: University of Leicester, School of Computing and Mathematical Sciences

Chapter Chapter 8 in Polynomial Diophantine Equations, 2024, pp 607-646 from Springer

Abstract: Abstract This chapter discusses various natural ways to order Diophantine equations. For example, one may order equations by length, defined as the sum of total degrees of its monomials plus the base 2 logarithm of the product of the absolute values of its coefficients. The chapter also introduces the so-called “canonical” ordering of Diophantine equations. For each of the discussed orderings, the chapter studies all polynomial Diophantine equations in that order and investigates which of them are solvable by the methods discussed in this book. The first open equations for each ordering are presented. The chapter ends with a big table collecting all open equations from the book in one place.

Date: 2024
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:978-3-031-62949-5_8

Ordering information: This item can be ordered from
http://www.springer.com/9783031629495

DOI: 10.1007/978-3-031-62949-5_8

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 ().