Markov Triples with Generalized Pell Numbers

Julieth F. Ruiz, Jose L. Herrera () and Jhon J. Bravo
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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

Mathematics, 2023, vol. 12, issue 1, 1-7

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.

Keywords: Markov equation; Markov triple; generalized Pell number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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