dc.contributor.author Rajasekaran, Aayush dc.date.accessioned 2018-04-30 17:00:17 (GMT) dc.date.available 2018-04-30 17:00:17 (GMT) dc.date.issued 2018-04-30 dc.date.submitted 2018-04-18 dc.identifier.uri http://hdl.handle.net/10012/13202 dc.description.abstract Additive number theory is the study of the additive properties of integers. Perhaps the best-known theorem is Lagrange’s result that every natural number is the sum of four squares. We study numbers whose base-k representations have certain interesting proper- ties. In particular, we look at palindromes, which are numbers whose base-k representations read the same forward and backward, and binary squares, which are numbers whose binary representation is some block repeated twice (like (36)_2 = 100100). en We show that all natural numbers are the sum of four binary palindromes. We also show that all natural numbers are the sum of three base-3 palindromes, and are also the sum of three base-4 palindromes. We also show that every sufficiently large natural number is the sum of four binary squares. We establish these results using virtually no number theory at all. Instead, we construct automated proofs using automata. The general proof technique is to build an appropriate machine, and then run decision algorithms to establish our theorems. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Automata Theory en dc.subject Number Theory en dc.subject Formal languages en dc.subject Automated proofs en dc.title Using Automata Theory to Solve Problems in Additive Number Theory en dc.type Master Thesis en dc.pending false uws-etd.degree.department David R. Cheriton School of Computer Science en uws-etd.degree.discipline Computer Science en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Shallit, Jeffrey uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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