Diophantine equations with Euler polynomials
نویسندگان
چکیده
منابع مشابه
Indecomposability of polynomials and related Diophantine equations
We present a new criterion for indecomposability of polynomials over Z. Using the criterion we obtain general finiteness result on polynomial Diophantine equation f(x) = g(y).
متن کاملDiophantine 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 کاملComplete decomposition of Dickson-type polynomials and related Diophantine equations
We characterize decomposition over C of polynomials f (a,B) n (x) defined by the generalized Dickson-type recursive relation (n ≥ 1), f (a,B) 0 (x) = B, f (a,B) 1 (x) = x, f (a,B) n+1 (x) = xf (a,B) n (x)− af (a,B) n−1 (x), where B, a ∈ Q or R. As a direct application of the uniform decomposition result, we fully settle the finiteness problem for the Diophantine equation f (a,B) n (x) = f (â,B̂)...
متن کاملDiophantine equations for second order recursive sequences of polynomials
Let B be a nonzero integer. Let define the sequence of polynomials Gn(x) by G0(x) = 0, G1(x) = 1, Gn+1(x) = xGn(x) +BGn−1(x), n ∈ N. We prove that the diophantine equation Gm(x) = Gn(y) for m,n ≥ 3, m 6= n has only finitely many solutions.
متن کاملReconstruction problems for graphs, Krawtchouk polynomials and Diophantine equations
We give an overview about some reconstruction problems in graph theory, which are intimately related to integer roots of Krawtchouk polynomials. In this context, Tichy and the author recently showed that a binary Diophantine equation for Krawtchouk polynomials only has finitely many integral solution. Here, this result is extended. By using a method of Krasikov, we decide the general finiteness...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2013
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa161-3-5