Additive Number Theory via Approximation by Regular Languages
Jason P. Bell, Thomas F. Lidbetter, Jeffrey O. Shallit · International Journal of Foundations of Computer Science · 2020
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 [Formula: see text] is the sum of at most three natural numbers whose base-[Formula: see text] representation has an equal number of [Formula: see text]’s and [Formula: see text]’s.