  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).
