Nonlinear identities and Diophantine equations involving balancing-like and Lucas-balancing-like numbers

DOI10.1007/s40590-022-00444-5zbMath1496.11017OpenAlexW4284879940MaRDI QIDQ2161100

Asim Patra, Bijan Kumar Patel, Claudio de J. Pita-Ruiz V.

Publication date: 4 August 2022

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-022-00444-5

zbMATH Keywords

Pell numbersPell-Lucas numbersDiophantine equationsbalancing-like numbersLucas-balancing-like numbers

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

• Diophantine equations concerning balancing and Lucas balancing numbers
• The diophantine equation \(x^ 4 - kx^ 2 y^ 2 + y^ 4 = 1\)
• Positive integer solutions of certain Diophantine equations
• Positive integer solutions of the Diophantine equation \(x^2-L_nxy+(-1)^ny^2=\pm 5^ r\)
• The Diophantine equation x⁴ - Dy² = 1, II
• Perfect Pell Powers
• Powers in products of terms of Pell's and Pell–Lucas Sequences
• Pell and Pell–Lucas Numbers with Applications
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