Additive Number Theory via Approximation by Regular Languages
Formal Languages and Automata Theory
2018-04-24 v1 Number Theory
Abstract
We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number > 25 is the sum of at most three natural numbers whose base-2 representation has an equal number of 0's and 1's.
Keywords
Cite
@article{arxiv.1804.07996,
title = {Additive Number Theory via Approximation by Regular Languages},
author = {Jason Bell and Thomas Finn Lidbetter and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1804.07996},
year = {2018}
}