**Goal:**

It can be proved that for any positive integer that is at least 24 there is a t such that the integer can be written as a sum of t positive integers with the property that their reciprocals sum up to 1.

For instance: 11 = 2 + 3 + 6 and 1/2 + 1/3 + 1/6 = 1.

The goal is to understand and explore this result. Since there are many open algorithmic questions, as written in the article by Köhler and Spilker (see below), it might be possible to discover new things.

Attention: this subject is based on an article written in German.

**Schedule:** To be determined.

**Supervisors:**
Gabor Wiese, Panagiotis Tsaknias

**Difficulty level:**
Introductory.

**Tools:**
Any computer language.

**Literature:**

- G. Köhler, J. Spilker: Harmonische Partitionen: Partitionen mit gegebener Summe der Kehrwerte der Teile. Mathematische Semesterberichte (2013), 60:67-80

**Results:**
[too be completed at the end of the project.]