On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

• Autorzy: D. Poulakis , P. G. Walsh
• Języki publikacji: EN

Abstrakty

EN

Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence {Tₙ}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence {Uₙ}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work of the second author.

Kategorie tematyczne

• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 1
• Strony: 51-55

Daty

wydano

2006

Twórcy

autor

D. Poulakis

• Department of Mathematics, Aristotle University of Thessaloniki, University Campus, 541 24 Thessaloniki, Greece

autor

P. G. Walsh

• Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, Ontario, Canada, K1N 6N5

Identyfikatory

DOI

10.4064/cm105-1-6