Elementary number-theoretical statements proved by Language Theory
Logic
2017-09-28 v1
Abstract
We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using -algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove that such a proof can be transformed into a traditional proof in . Finally, we show some examples of non-trivial number-theoretical theorems that can be proved by formal languages in a natural way. These number-theoretical results concern densely divisible numbers, semi-perimeters of Pythagorean triangles, middle divisors and partitions into consecutive parts.
Cite
@article{arxiv.1709.09617,
title = {Elementary number-theoretical statements proved by Language Theory},
author = {José Manuel Rodríguez Caballero},
journal= {arXiv preprint arXiv:1709.09617},
year = {2017}
}