Add to ORKGGiven an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 +· · ·+ak, a1, . . . , ak ¿ A, is not constant for n large enough. This result is a corollary of our main theorem, which partially answers a question of S´ark¨ozy and S´os on representation functions for multivariate linear forms. Additionally, we obtain an Erd¿os-Fuchs type result for a wide variety of representation functions
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
Given an infinite sequence of positive integers A, we prove that for every nonnegative integer k the...
We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of p...
AbstractLet A={a1,a2,…}(a1<a2<⋯) be an infinite sequence of nonnegative integers. Let k≥2 be a fixed...
We prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers suc...
AbstractLet A be an infinite subset of natural numbers, n∈N and X a positive real number. Let r(n) d...
We consider systems of polynomial equations and inequalities to be solved in integers. By applying t...
While in the univariate case solutions of linear recurrences with constant coefficients have rationa...
The inverse problem for representation functions takes as input a triple (X,f,L), where X is a count...
AbstractFor a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respect...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
Given an infinite sequence of positive integers A, we prove that for every nonnegative integer k the...
We prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of p...
AbstractLet A={a1,a2,…}(a1<a2<⋯) be an infinite sequence of nonnegative integers. Let k≥2 be a fixed...
We prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers suc...
AbstractLet A be an infinite subset of natural numbers, n∈N and X a positive real number. Let r(n) d...
We consider systems of polynomial equations and inequalities to be solved in integers. By applying t...
While in the univariate case solutions of linear recurrences with constant coefficients have rationa...
The inverse problem for representation functions takes as input a triple (X,f,L), where X is a count...
AbstractFor a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respect...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...