On square classes in generalized Fibonacci sequences

• Autorzy: Zafer Şiar , Refik Keskin
• Języki publikacji: EN

Abstrakty

EN

Let P and Q be nonzero integers. The generalized Fibonacci and Lucas sequences are defined respectively as follows: U₀ = 0, U₁ = 1, V₀ = 2, V₁ = P and $U_{n+1} = PUₙ + QU_{n-1}$, $V_{n+1} = PVₙ + QV_{n-1}$ for n ≥ 1. In this paper, when w ∈ {1,2,3,6}, for all odd relatively prime values of P and Q such that P ≥ 1 and P² + 4Q > 0, we determine all n and m satisfying the equation Uₙ = wUₘx². In particular, when k|P and k > 1, we solve the equations Uₙ = kx² and Uₙ = 2kx². As a result, we determine all n such that Uₙ = 6x².

Kategorie tematyczne

• 11B37: Recurrences
• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 174
• Numer: 3
• Strony: 277-295

Daty

wydano

2016

Twórcy

autor

Zafer Şiar

• Mathematics Department, Bingöl University, 12000 Bingöl, Turkey

autor

Refik Keskin

• Mathematics Department, Sakarya University, 54050 Sakarya, Turkey

Identyfikatory

DOI

10.4064/aa8436-4-2016