SUBJECT
Title
Combinatorial number theory
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Brun's sieve and its applications. Schnirelmann's addition theorems, the primes form an additive basis. Additive and multiplicative Sidon sets. Divisibility properties of sequences, primitive sequences. The "larger sieve", application. Hilbert cubes in dense sequences, applications. The theorems of van der Waerden and Szemeredi on arithmetic progressions. Schur's theorem on the Fermat congruence.
Readings
- H. Halberstam, K. F. Roth: Sequences.
- C. Pomerance, A. Sárközy: Combinatorial Number Theory (in: Handbook of Combinatorics)
- P. Erdős, J. Surányi: Topics in number theory.