Description
Dear Colleague,
It is our pleasure to invite you to the next talk in our Online Number Theory Seminar, on
25 October (Friday) at 17:00 CET (8:00 PDT, 11:00 EDT, 15:00 GMT, 18:00 Israel Daylight Time, 20:30 Indian Standard Time; already Saturday 2:00 AEDT, 4:00 NZDT)
Speaker: K. Gyarmati (Eötvös Loránd University)
Title: Combinatorics and Diophantine equations
Abstract: In this talk, we apply combinatorics to study problems related to Diophantine-type equations. In the first part, we study the cardinality of such sets of squares in which the difference between any two squares is also a square. Such a set with $m$ elements is called a Diophantine square $m$-tuple. For example, we will see that there are infinitely many Diophantine square triples. It is also proved that there is no Diophantine square triple that only contains squares of Fibonacci numbers. The second part of the talk is a joint work with my colleague Katalin Fried. We say that a set $\mathcal B\subseteq\mathbb Z$ forms a multiplicative basis of order $h$ of $\mathcal S$ if every element of $\mathcal S$ can be written as the product of $h$ members of $\mathcal B$. We give non-trivial lower bounds for the size of multiplicative basis of order 2 of the set $\{f(1),f(2),\dots,f(n)\}$ where $f(x)\in\mathbb Z[x]$ is a polynomial. We also study generalizations of these problems.
Meeting link: https://unideb.webex.com/unideb/j.php?MTID=md9323ab2e0a9b156528a123d177243a1
Meeting number: 2783 434 8348
Please, share the link with colleagues who are interested, tell us if you have a proposal for a talk, and
also inform us in case you are not willing to receive announcements of these events. The email address of the
seminar is ntrg@science.unideb.hu . We keep the program updated at https://ntrg.math.unideb.hu/seminar.html ,
where (upon the agreement of the Speaker), you can also find the video and the slides of the talk.
We are looking forward to meeting you, with kind regards,
the organizers (K.Győry, Á.Pintér, L.Hajdu, A.Bérczes, Sz.Tengely, I.Pink, Debrecen Number Theory Research Group , University of Debrecen)