# Lagrange's Theorem for Binary Squares

@article{Madhusudan2018LagrangesTF, title={Lagrange's Theorem for Binary Squares}, author={P. Madhusudan and Dirk Nowotka and Aayush Rajasekaran and Jeffrey Shallit}, journal={ArXiv}, year={2018}, volume={abs/1710.04247} }

We show how to prove theorems in additive number theory using a decision procedure based on finite automata. Among other things, we obtain the following analogue of Lagrange's theorem: every natural number > 686 is the sum of at most 4 natural numbers whose canonical base-2 representation is a binary square, that is, a string of the form xx for some block of bits x. Here the number 4 is optimal. While we cannot embed this theorem itself in a decidable theory, we show that stronger lemmas that…

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## 6 Citations

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