Sums of squares of integers from residue classes
Abstract
A subset [Formula: see text] is called s-almost square universal if every sufficiently large positive integer can be written as a sum of at most s squares of integers from [Formula: see text]. In this paper, we study the minimal number [Formula: see text] with this property, where [Formula: see text] denotes the residue class of d modulo m, with [Formula: see text] and [Formula: see text]. We further prove that [Formula: see text] is s-square universal for some [Formula: see text] if and only if [Formula: see text], and determine the minimal such number [Formula: see text] in these cases.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 07
- Pages
- 1617–1636
- Publication date
- 21 April 2026
- Language
- EN