Description
Dear Colleague,
It is our pleasure to invite you to the next talk in our Online Number Theory Seminar, on
8 November (Friday) at 17:00 CET (8:00 PST, 11:00 EST, 16:00 GMT, 18:00 IST, 21:30 India Standard Time; already Saturday 3:00 AEDT, 5:00 NZDT)
Speaker: A. Togbé (Purdue University Northwest)
Title: On $P$-integers and generalizations
Abstract: For an integer $k>1$, let $\varphi(k)$ denote Euler's totient function and $\omega(k)$ the number of distinct prime divisors of $k$. We say that $k$ is a $P$-integer if the first $\varphi(k)$ primes coprime to $k$ form a reduced residue system modulo $k$. In 1978, Recaman asked the following question:
{\it Are there only finitely many primes which are $P$-integers?} \\
In 1980, Pomerance answer this question by proving the finiteness of the set of $P$-integers. Moreover, he conjectured that
if $k$ is a $P$-integer, then $k\leq 30$.
During this talk, we will discuss not only the progress towards the proof of this conjecture but also its generalizations.
Meeting link: https://unideb.webex.com/unideb/j.php?MTID=m7f7e9c0bdea9651ef638c5b00a515136
Meeting number: 2794 390 5264
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)