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Balanced factorisations | | Anton A. Klyachko
; Anton N. Vassilyev
; | | Date: |
4 Jun 2015 | | 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. However, it is unknown whether the
word "several" can be replaced with "four". 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. | | Source: | arXiv, 1506.1571 | | Services: | Forum | Review | PDF | Favorites | |
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