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Markov Triples with Generalized Pell Numbers

Author

Listed:
  • Julieth F. Ruiz

    (Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4-70, Popayán 190003, Colombia)

  • Jose L. Herrera

    (Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4-70, Popayán 190003, Colombia)

  • Jhon J. Bravo

    (Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4-70, Popayán 190003, Colombia)

Abstract

For an integer k ≥ 2 , let ( P n ( k ) ) n be the k -generalized Pell sequence which starts with 0 , … , 0 , 1 ( k terms), and each term afterwards is given by P n ( k ) = 2 P n − 1 ( k ) + P n − 2 ( k ) + ⋯ + P n − k ( k ) . In this paper, we determine all solutions of the Markov equation x 2 + y 2 + z 2 = 3 x y z , with x , y , and z being k -generalized Pell numbers. This paper continues and extends a previous work of Kafle, Srinivasan and Togbé, who found all Markov triples with Pell components.

Suggested Citation

  • Julieth F. Ruiz & Jose L. Herrera & Jhon J. Bravo, 2023. "Markov Triples with Generalized Pell Numbers," Mathematics, MDPI, vol. 12(1), pages 1-7, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:108-:d:1309217
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