A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation

Ralph Høibakk, Dag Lukkassen, Annette Meidell and Lars-Erik Persson
Additional contact information
Ralph Høibakk: Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway
Dag Lukkassen: Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway
Annette Meidell: Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway
Lars-Erik Persson: Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, 8514 Narvik, Norway

Mathematics, 2020, vol. 8, issue 2, 1-21

Abstract: The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation z 4 − 2 L z 3 + ( L 2 − a 2 − b 2 ) z 2 + 2 L a 2 z − L 2 a 2 = 0 are developed. For the case L ≥ L min , these methods imply a complete parametric representation for integer solutions of SLP in the first quadrant. Some corresponding (less complete) results for the case L > L min are also pointed out.

Keywords: single ladder problem (SLP); integer parametric solutions; simultaneous quadratic equations; quartic equations; algebraic equations; recreational mathematics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/267/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/267/ (text/html)

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:gam:jmathe:v:8:y:2020:i:2:p:267-:d:321817

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().