Arithmetic properties of q-Fibonacci numbers and q-pell numbers

نویسنده

  • Hao Pan
چکیده

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A NOTE ON SUM OF k-TH POWER OF HORADAM’S SEQUENCE

(1) wn+2 = pwn+1 + qwn, with given w0 = a,w1 = b and n ≥ 0. This sequence was introduced, in 1965, by Horadam [Ho], and it generalizes many sequences (see [HW, HM]). Examples of such sequences are Fibonacci numbers sequence (Fn)n≥0, Lucas numbers sequence (Ln)n≥0, and Pell numbers sequence (Pn)n≥0, when one has p = q = b = 1, a = 0; p = q = b = 1, a = 2; and p = 2, q = b = 1, a = 0; respectivel...

متن کامل

A Note on Stability of an Operator Linear Equation of the Second Order

and Applied Analysis 3 If p, 1/q ∈ Z, then solutions f : N0 → Z of the difference equation 1.7 are called the Lucas sequences see, e.g., 24 ; in some special cases they are given specific names; that is, the Fibonacci numbers p −1, q −1, f 0 0, and f 1 1 , the Lucas numbers p −1, q −1, f 0 2, and f 1 1 , the Pell numbers p −2, q −1, f 0 0, and f 1 1 , the Pell-Lucas or companion Lucas numbers p...

متن کامل

Congruences for q-Lucas Numbers

For α, β, γ, δ ∈ Z and ν = (α, β, γ, δ), the q-Fibonacci numbers are given by F ν 0 (q) = 0, F ν 1 (q) = 1 and F ν n+1(q) = q αn−βF ν n (q) + q γn−δF ν n−1(q) for n > 1. And define the q-Lucas number Ln(q) = F ν n+1(q)+ q γ−δF ν∗ n−1(q), where ν∗ = (α, β− α, γ, δ − γ). Suppose that α = 0 and γ is prime to n, or α = γ is prime to n. We prove that Ln(q) ≡ (−1) (mod Φn(q)) for n > 3, where Φn(q) i...

متن کامل

NEW CONNECTION FORMULAE BETWEEN (p, q)−FIBONACCI POLYNOMIALS AND CERTAIN JACOBI POLYNOMIALS

The main purpose of this article is to solve the connection problems between (p, q)−Fibonacci polynomials and the two polynomials, namely Chebyshev polynomials of third and fourth kinds which are considered as two nonsymmetric polynomials of the Jacobi polynomials. Moreover, the inversion connection formulae for the latter formulae are given. We show that all the connection coefficients are exp...

متن کامل

New families of Jacobsthal and Jacobsthal-Lucas numbers

In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 306  شماره 

صفحات  -

تاریخ انتشار 2006