Covering Systems and Periodic Arithmetical Functions
نویسندگان
چکیده
If the ring Z of integers is the union of finitely many residue classes a1(mod n1), . . . , ak(mod nk), then the system A = {as(mod ns)}s=1 is called a cover of Z or a covering system. There are many problems and results on this topic initiated by Paul Erdös. In this talk we introduce progress on the main open problems in this field, as well as the algebraic theory of periodic arithmetical maps motivated by the speaker’s research on covering systems. The talk is related to number theory, combinatorics, algebraic structures and special functions. Perhaps my favorite problem of all concerns covering systems.
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