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

Author

Listed:
  • 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
    Department of Mathematics and Computer Science, Karlstad University, 651 88 Karlstad, Sweden)

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.

Suggested Citation

  • Ralph Høibakk & Dag Lukkassen & Annette Meidell & Lars-Erik Persson, 2020. "A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:267-:d:321817
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