Diophantine equations with products of consecutive terms in Lucas sequences II

نویسنده

  • Florian Luca
چکیده

Here, we continue our work from [7] and study an inhomogeneous variant of a Diophantine equation concerning powers in products of consecutive terms of Lucas sequences. AMS Subject Classification: 11L07, 11N37, 11N60

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

Diophantine Equations Related with Linear Binary Recurrences

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

متن کامل

1 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 ON THE INTERSECTIONS OF FIBONACCI , PELL , AND LUCAS NUMBERS

We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)}n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V -sequences when the product of their discriminants is a perfect square. Moreover, the inter...

متن کامل

INFINITELY MANY POSITIVE INTEGER SOLUTIONS OF THE QUADRATIC DIOPHANTINE EQUATIONS x 2 − 8 B

In this study, we consider the quadratic Diophantine equations given in the title and determine when these equations have positive integer solutions. Moreover, we find all positive integer solutions of them in terms of Balancing numbers Bn, Pell and Pell-Lucas numbers, and the terms of the sequence {vn} , where {vn} is defined by v0 = 2, v1 = 6, and vn+1 = 6vn − vn−1 for n ≥ 1.

متن کامل

On the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn

In this paper, we find all the solutions of the Diophantine equation x + 2 513 = y in nonnegative integers x, y, α, β, γ, n ≥ 3 with x and y coprime. In fact, for n = 3, 4, 6, 8, 12, we transform the above equation into several elliptic equations written in cubic or quartic models for which we determine all their {2, 5, 13}-integer points. For n ≥ 5, we apply a method that uses primitive diviso...

متن کامل

Complete decomposition of Dickson-type recursive polynomials and a related Diophantine equation

We characterize decomposition over C of polynomials fn(x) defined by the generalized Dicksontype recursive relation f0(x) = B, f1(x) = x, fn+1(x) = xfn(x)− afn−1(x) (n ≥ 1), where B, a ∈ Q or R. This parametric class of polynomials includes Fibonacci, Pell, Fermat, Dickson, Lucas (w-), Pell-Lucas, Fermat-Lucas polynomials as well as Chebyshev polynomials of the first and second kind. As an appl...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007