Description
Dear Colleague,
It is our pleasure to invite you to the next talk in our Online Number Theory Seminar, on
14 June (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: T. Miyazaki (Gunma University)
Title: Number of solutions to a special type of unit equations in two unknowns III
Abstract: This talk is a continuation of the one presented by the speaker on November 25, 2022. It is conjectured that for any fixed relatively prime
positive integers $a, b$ and $c$ all greater than 1 there is at most one solution to the equation $a^x + b^y = c^z$ in positive integers $x, y$ and $z,$ except
for specific cases. In this talk we give a brief introduction to the conjecture highlighting the contents of Part II, and present our results with
their proofs. In particular we find some, presumably infinitely many, new values of $c$ with the property that for each such c the conjecture
holds true, except for only finitely many pairs of $a$ and $b.$ Most importantly we prove that if $c = 13$ then the equation has at most one
solution, except for $(a, b) = (3, 10)$ or $(10, 3)$ each of which gives exactly two solutions. This is a joint work with I. Pink.
Meeting link: https://unideb.webex.com/unideb/j.php?MTID=m0fa8547054ca0e2d3f07f480eaa217ba
Meeting number: 2733 496 0864
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)