Jean-Marie De Koninck has been a researcher and professor of mathematics at Université Laval (Québec) for more than forty years and is well known to the scientific community for his work in analytic number theory. He is the author of 18 books and 163 peer reviewed articles in scientific journals. He is now Professor Emeritus. Professor De Koninck has also hosted his own science outreach television show "C'est mathématique!", broadcasted on the French-Canadian channel (Canal Z) 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 as the founder of Operation Red Nose, a road safety operation involving over 55,000 volunteers across Canada. He was also very active in the media during the ten years he acted as President of the Table québécoise de la sécurité routière. He is now a member of the Board for the Société de l'assurance automobile du Québec. Many have also seen him as a color-commentator for nationally televised swim events.

AG 1, AG 2, AG 3, INET, AG 4, AG 5, D6, SWS, RG1, MMCI   Info

AG Audience

English

90 Minutes

Saarbrücken

Given an integer n ≥ 2, let P (n) stand for its largest prime factor. Given integers k ≥ 2 and ℓ ≥ 2, consider the set Ek,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. For instance, the smallest element of E3,2 is 1 294 298, the smallest known element of E3,3 has 77 digits and no elements of E4,2 are known, even though all these sets are believed to be infinite. In this talk, using elementary, analytic and probabilistic approaches, we will shed some light on these sets and raise several open problems. This is joint work with Nicolas Doyon, Florian Luca and Matthieu Moineau.

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This talk will be a hybrid event. You can join the meeting in E1 5 room 002 in Saarbrücken, in G26 room 111 in Kaiserlautern or via Zoom. Please contact the Office team for Zoom link information.

Annika Meiser

+49 681 9303 9105

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Yes

Kaiserslautern

G26

111

SWS Space 2 (6312)