This proceedings volume, the fifth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 19th annual workshop, held online due to the COVID-19 pandemic.

Preface.- 1. On the Number of Dot Product Chains in Finite Fields and Rings (V. Blevins, D. Crosby, E. Lynch, S. Senger).- 2. Completeness of Positive Linear Recurrence Sequences (E. Boldyriew, J. Haviland, P. Lam, J. Lentfer, S.J. Miller, F.T. Suarez).- 3. Length Density and Numerical Semigroups (C. Brower, S. Chapman, T. Kulhanek, J. McDonough, C. O'Neill, V. Pavlyuk, V. Ponomarenko).- 4. On a Problem of Cilleruelo-Nathanson, II (Y.-G. Chen, J. Fang).- 5. Linked Partition Ideals and a Schur-type Identity of Andrews (S. Chern).- 6. Semi-magic Matrices for Dihedral Groups (R. Donley).- 7. Is the Syracuse Falling Time Bounded by 12? (S. Eliahou, J. Fromentin, R. Simonetto).- 8. Genera of Numerical Semigroups and Polynomial Identities for Degrees of Syzygies (L. Fel).- 9. Expansion, Divisibility, and Parity (H.A. Helfgott).- 10. Sums of Squares (R.J. Hendel).- 11. Bilinear Generalized Radon Transforms in the Plane (A. Greenleaf, A. Iosevich, B. Krause, A. Liu).- 12. GeneralizedBernoulli Numbers, Cotangent Power Sums, and Higher-order Arctangent Numbers (B. Isaacson).- 13. A New Class of Minimal Asymptotic Bases (M.B. Nathanson).- 14. An Inverse Problem for Infinite Sidon Sets (M.B. Nathanson).

This proceedings volume, the fifth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 19th annual workshop, held online due to the COVID-19 pandemic. Organized every year since 2003 by the New York Number Theory Seminar at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. The CANT 2021 meeting featured over a hundred speakers from North and South America, Europe, Asia, Australia, and New Zealand, and was the largest CANT conference in terms of the number of both lectures and participants.
These proceedings contain peer-reviewed and edited papers on current topics in number theory. Topics featured in this volume include sumsets, minimal bases, Sidon sets, analytic and prime number theory, combinatorial and discrete geometry, numerical semigroups, and a survey of expansion, divisibility, and parity. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

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