Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.
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Table of Contents1. Sukumar Das Adhikari and Shalom Eliahou, "On a conjecture of Fox andKleitman on the degree of regularity of a certain linear equation".- 2.Béla Bajnok, \Open problems about sumsets in finite abelian groups: Minimum sizes and critical numbers".- 3.Andrew Best, Pat&rick Dynes, Xixi Edelsbrunner, Brian McDonald, StevenJ. Miller, Kimsy Tor, Caroline Turnage-Butterbaugh and Madeleine Weinstein, "Benford behavior of generalized Zeckendorf decompositions".- 4.Andrew Best, Karen Huan, Nathan McNew, Steven J. Miller, Jasmine.Powell, Kimsy Tor, and Madeleine Weinstein, "Ramsey theory problemsover the integers: Avoiding generalized progressions".- 5.Dakota Blair, "Recurrence identities of b-ary partitions".- 6.Lisa Bromberg, "Hashing with SL(2;Fp) and some applications to information security".- 7.Hannah Constantin, Ben Houston-Edwards, and Nathan Kaplan, "Numerical sets, core partitions, and integer points in polytopes".- 8.David Covert and Steven Senger, "Pairs of dot products in finite fields andrings".- 9.Charles Helou, "Characteristic, counting, and representation functions.- 10.&nbWilnliam J. Keith, \Partitions into parts simultaneously regular, distinct,and/or flat".- 11.Mizan R. Khan and Karen M. Rogers, "An exposition of White's characterization of empty lattice tetrahedra".- 12.Urban Larsson, \A misèere-play ?-operator".- 13. Jaewoo Lee, "A new proof of Khovanski's theorem on the geometry of sumsets.- 14.;Kieren MacMillan and Jonathan Sondow, "Initial sums of the Legendresymbol: Is min+max 0 ?".- 15.Brendan Murphy and Giorgis Petridis, "A second wave of expanders in finite fi elds".- 16.Melvyn B. Nathanson, "The Erd}os paradox".- 17.Melvyn B. Nathanson, "Limits and decomposition of de Bruijn's additive systems".- 18.Jonathan Sondow, "Extending Babbage's (non-)primality tests".- 19.Zhi-Wei Sun, "Conjectures on representations involving primes".