Jean-Marie De Koninck

(Université Laval)
hosted by Joël Ouaknine

"Consecutive integers divisible by a power of their largest prime factor"

( MPI-SWS talk in Kooperation mit dem Fachbereich Informatik)

Given an integer n ≥ 2, let P (n) stand for its largest prime factor. Given integers k ≥ 2 and ℓ ≥ 2, consider the setEk,ℓ of those integers n ≥ 2 for which P (n + i)ℓ | n + i for i = 0, 1, . . . , k. Each of these sets is very small. Forinstance, the smallest element of E3,2 is 1 294 298, the smallest known element of E3,3 has 77 digits and no elements ofE4,2 are known, even though all these sets are believed to be infinite. In this talk, using elementary, analytic andprobabilistic approaches, we will shed some light on these sets and raise several open problems. This is joint work withNicolas Doyon, Florian Luca and Matthieu Moineau.

Bio: Jean-Marie De Koninck has been a researcher and professor of mathematics at Université Laval (Québec) for more thanforty years and is well known to the scientific community for his work in analytic number theory. He is the author of 18books and 163 peer reviewed articles in scientific journals. He is now Professor Emeritus. Professor De Koninck has alsohosted his own science outreach television show "C'est mathématique!", broadcasted on the French-Canadian channel (CanalZ) and later on TFO (Télévision française de l'Ontario). In 2005, he created the Sciences and Mathematics in Action(SMAC) program whose purpose is to excite kids about science and mathematics. He is well known by the general public asthe founder of Operation Red Nose, a road safety operation involving over 55,000 volunteers across Canada. He was alsovery active in the media during the ten years he acted as President of the Table québécoise de la sécurité routière. Heis now a member of the Board for the Société de l'assurance automobile du Québec. Many have also seen him as acolor-commentator for nationally televised swim events.

Time: Monday, 11.07.2022, 14:00
Place: MPI-SWS Saarbrücken, E1 5, room 002

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