Polynomial values in linear recurrences, II
نویسندگان
چکیده
منابع مشابه
Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients
We present an algorithm which, given a linear recurrence operator L with polynomial coefficients, m ∈ N \ {0}, a1, a2, . . . , am ∈ N \ {0} and b1, b2, . . . , bm ∈ K, returns a linear recurrence operator L ′ with rational coefficients such that for every sequence h,
متن کاملHypergeometric Solutions of Linear Recurrences with Polynomial Coefficents
Let K be a field of characteristic zero . We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations . Let KN denote the ring of all sequences over K, with addition and multiplication defined term-wise . Following Stanley (1980) we identify two sequences if they agree from some point on . Forma...
متن کاملPolynomial Recurrences and Cyclic Resultants
Let K be an algebraically closed field of characteristic zero and let f ∈ K[x]. The m-th cyclic resultant of f is rm = Res(f, x m − 1). A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds. We prove that a generic monic polynomial of degree d is determined by its first 2d+1 cy...
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 کاملLinear Equations over Multiplicative Groups, Recurrences, and Mixing II
Let u1, . . . , um be linear recurrences with values in a field K of positive characteristic p. We show that the set of integer vectors (k1, . . . , km) such that u1(k1) + · · ·+ um(km) = 0 is p-normal in a natural sense generalizing that of the first author, who proved the result for m = 1. Furthermore the set is effectively computable if K is. We illustrate this with an example for m = 4. We ...
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: Journal of Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90056-9