Balanced factorisations
Rings and Algebras
2020-07-20 v3 Commutative Algebra
History and Overview
Number Theory
Abstract
Any rational number can be factored into a product of several rationals whose sum vanishes. This simple but nontrivial fact was suggested as a problem on a maths olympiad for high-school students. We completely solve similar questions in all finite fields and in some other rings, e.g., in the complex and real matrix algebras. Also, we state several open questions.
Cite
@article{arxiv.1506.01571,
title = {Balanced factorisations},
author = {Anton A. Klyachko and Anton N. Vassilyev},
journal= {arXiv preprint arXiv:1506.01571},
year = {2020}
}
Comments
7 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm