Monday, December 2, 2013

An analogue of the Proth-Gilbreath conjecture (new paper)

O fenomenologie a numerelor prime - in gen fantasy cu demonstratii plus "experiment" (computer).

Far East Journal of Mathematical Sciences (FJMS)
Volume 81, Issue 1, Pages 1 - 12 (October 2013)
Mihai Caragiu, Alexandru Zaharescu and Mohammad Zaki
Communicated by Juliusz Brzezinski

Sunday, September 29, 2013

Miami University Fall Conference on Undergraduate Research in Mathematics

Abstract of my presentation:

More than twelve years ago, a talk on "Ducci games" delivered jointly by two Ohio Northern University students at the 2001 Ohio MAA Spring meeting initiated a fairly long streak of undergraduate research in the area of number theory at our school. Since then, Ohio Northern University students presented 40 talks and posters in the broad area of number theory at various mathematics meetings, and were co-authors of 11 research articles in number theory which appeared in peer-reviewed mathematics journals. We were especially pleased to see our research on "greatest prime factor sequences" (published in Fibonacci Quarterly in 2010) featured alongside other "noteworthy variations on the Fibonacci numbers" in the keynote talk at the 15th International Conference on Fibonacci Numbers held in Budapest (June 25-30, 2012), and cited in various other journals. In the light of the speaker's experience as an undergraduate research advisor, we will try to address some issues of interest regarding the impact of undergraduate research in the outside mathematical community. This "impact" may be viewed as a long-sought fulfillment or closure of the combined efforts of faculty and students engaged in undergraduate research, which ultimately takes a life of its own. We will explore open-ended difficult questions such as: What does it mean to make an impact? Are there specific strategies for smaller schools? Can presentations make an impact? What is the relationship between undergraduate research and faculty research? Is it harder for pure mathematics?

Tuesday, August 6, 2013

Alba Iulia 2013

My talk (abstract) at the 2013 RMS-AMS Special Session of Discrete Mathematics and Theoretical Computer Science in Alba Iulia:
Uniform distribution for a class of k-paradoxical oriented graphs 
By using estimates for incomplete character sums with polynomial arguments, we provide uniform distribution results for the dominating sets in a class of k-paradoxical regular oriented graphs, including the Paley tournaments. Moreover, we will explore a method of quasi-random tournament generation from fi nite sets of natural numbers, by using the greatest prime factor function.

Thursday, July 18, 2013

Work on Stirling numbers honored with an Allendoerfer Award (2013)

Khristo N. Boyadzhiev (Ohio Northern University) - 2013 Carl B. Allendoerfer Award for the paper "Close Encounters with the Stirling Numbers of the Second Kind" - Mathematics Magazine, 85:4 (2012), pp. 252-266.
More at:


Mihai Caragiu, Donald Pleshinger and Jonathan C. Schroeder, UNIFORM DISTRIBUTION FOR A CLASS OF k‑PARADOXICAL ORIENTED GRAPHS, JP Journal of Algebra, Number Theory and Applications, Volume 29, Issue 2, Pages 107-117 (June 2013)

Monday, January 14, 2013