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arXiv · 1709.09617

Elementary number-theoretical statements proved by Language Theory

José Manuel Rodríguez Caballero
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Abstract

We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $σ$-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 $\textbf{ZFC}$. 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.

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BibTeXRIS

José Manuel Rodríguez Caballero. 2017-09-27. Elementary number-theoretical statements proved by Language Theory. https://arxiv.org/abs/1709.09617

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