IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-62949-5_7.html
   My bibliography  Save this book chapter

Existence of Integer Solutions

In: Polynomial Diophantine Equations

Author

Listed:
  • Bogdan Grechuk

    (University of Leicester, School of Computing and Mathematical Sciences)

Abstract

The size of a polynomial with integer coefficients is computed by replacing each coefficient by its absolute value and evaluating the resulting polynomial at 2. This chapter investigates whether Diophantine equations have any integer solutions at all (Hilbert 10th Problem). The chapter starts with elementary methods like the integral Hasse principle, but then proceed to more advanced methods, such as the use of Jacobi symbol or the analysis of possible prime divisors of cubic polynomials. The chapter ends with a discussion of which equations are solvable in positive integers.

Suggested Citation

  • Bogdan Grechuk, 2024. "Existence of Integer Solutions," Springer Books, in: Polynomial Diophantine Equations, chapter 0, pages 537-606, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-62949-5_7
    DOI: 10.1007/978-3-031-62949-5_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-62949-5_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.