Project 13: "Additive and combinatorial number theory"

This project is running since 2015.

Principal investigator: Christian Elsholtz
Graz University of Technology, Austria.
Mentor for: Ddamulira, Wiegel, Technau; Iaco, Kreso, Smertnig.

DK Student

Project description

I am particularly interested in the interplay of additive and multiplicative questions. The methods used are often a combination of tools from combinatorics and analytic number theory.

Topics that were studied in this project include:

1) Number of solutions of Diophantine equation, e.g. the equation
1=1/x_1+ ... + 1/x_k, in integers x_i.

2) questions what happens if one adds prime numbers to a thin sequence, such as powers of 2?

3) Constructing large sets of integers such that no a_i divides a sum a_j+a_k.