Combinatorial and additive number theory III : CANT New York USA 2017 and 2018 Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York these proceedings offer 17 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. Topics featured in this volume include sumsets partitions convex polytopes and discrete geometry Ramsey theory commutative algebra and discrete geometry and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory. . Preface 1. S.D. Adhikari B. Roy S. Sarkar: Weighted Zero Sums for Some Finite Abelian Groups of Higher Ranks 2. S. Akhtari: Counting Monogenic Cubic Orders 3. P. Baird Smith A. Epstein K. Flint S.J. Miller: The Zeckendorf Game 4. H.P. Chaos C.E. Finch Smith: Iterated Riesel and Iterated Sierpinski Numbers 5. M. Desgrottes S. Senger D. Soukup R. Zhu: A General Framework for Studying Finite Rainbow Configurations 6. M. DiNasso: Translation Invariant Filters and van der Waerdens Theorem 7. R.W. Donley Jr.: Central Values for Clebsch Gordan Coefficients 8. L.G. Fel: Numerical Semigroups Generated by Squares and Cubes of Three Consecutive Integers 9. I. Goldbring S. Leth: On Supra sim Sets of Natural Numbers 10. S. Han A.M. Masuda S. Singh J. Thiel: Mean Row Values in (u.v) Calkin Wilf Trees 11. M.B. Nathanson: Dimensions of Monomial Varieties 12. Matrix Scaling Limits in Finitely Many Iterations (M.B. Nathanson) 13. M.B. Nathanson: Not All Groups are LEF Groups or Can You Know if a Group is Infinite 14. A. Rice: Binary Quadratic Forms in Difference Sets 15. D.A. Ross: Egyptian Fractions Non Archimedean Ordered Field Nonstandard Analysis 16. A. Rukhin: A Dual Radix Approach to Steiners 1 Cycle Theorem 17. Y. Tschinkel K. Yang: Potentially Stably Rational del Pezzo Surfaces Over Nonclosed Fields.