### 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

**Second phase of the doctoral program:**-
**Stefan Planitzer**(Austria; since July 2015)

*Email*: stefan.planitzer@student.tugraz.at

*Mentors*: Robert Tichy, Daniel Krenn.

### 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.