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Representation functions in the set of natural numbers
Shi-Qiang Chen, Csaba Sándor, Quan-Hui Yang
Let be the set of all nonnegative integers. For and , let denote the number of solutions of the equation , $s…
Multiplicative complements II
Anett Kocsis, Dávid Matolcsi, Csaba Sándor +1
In this paper we prove that if and are infinite subsets of positive integers such that every positive integer can be written as , , , then $\displ…
Unique representations of integers by linear forms
Sándor Z. Kiss, Csaba Sándor
Let be an integer and let be a set of nonnegative integers. For a -tuple of positive integers with $1 \le λ_{1} < λ_{2} < \d…
On monotone increasing representation functions
Sándor Z. Kiss, Csaba Sándor, Quan-Hui Yang
Let be an integer and let be a set of nonnegative integers. The representation function for the set is the number of representations of a nonnegative…
On a problem of Nathanson related to minimal asymptotic bases of order
Shi-Qiang Chen, Csaba Sándor, Quan-Hui Yang
For integer and , we define to be all integers which can be written as a sum of elements of . The set is called an asymptotic basis o…
Lagrange-like spectrum of perfect additive complements
Balázs Bárány, Jin-Hui Fang, Csaba Sándor
Two infinite sets and of non-negative integers are called \emph{perfect additive complements of non-negative integers}, if every non-negative integer can be uniquely expres…