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We introduce a method to derive theorems from Elementary Number Theory bymeans of relationships among formal languages. Using $\sigma$-algebras, wedefine 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-trivialnumber-theoretical theorems that can be proved by formal languages in a naturalway. These number-theoretical results concern densely divisible numbers,semi-perimeters of Pythagorean triangles, middle divisors and partitions intoconsecutive parts.

Elementary number-theoretical statements proved by Language Theory