30 years of collaboration
Clemens Fuchs, Lajos Hajdu

TL;DR
This paper reviews 30 years of collaboration between Austrian and Hungarian number theorists, highlighting key results and focusing on problems related to polynomial squares and the unit sum number problem.
Contribution
It provides a curated overview of significant results from a long-standing collaboration, emphasizing two specific open problems in number theory.
Findings
Discussion of a conjecture by Rényi and Erdős on polynomial squares
Analysis of Zelinsky's question on the unit sum number problem
Presentation of selected interesting data and results
Abstract
We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of R\'enyi and Erd\H{o}s (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem), which will be presented in turn. This paper evolved from a plenary invited talk that the authors gave at the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Gy\H{o}r (Hungary).
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Cryptography and Residue Arithmetic
