Lundi 8 décembre 2014, 09h30 / Monday, December 8, 2014, 9:30 am

The ranges of some familiar functions

Résumé/Abstract : Consider those integers which appear as values of the sum-of-divisors function, of Euler's function (returning the order of the multiplicative group mod n), or of Carmichael's function (returning the exponent of that group). That most numbers are never values of these functions is not immediately obvious (especially so for Carmichael's function). Studying the problem for Euler's function 80 years ago, Erdos was led to discover the normal number of prime factors of a shifted prime. This talk will survey the subject and discuss some very new results.

Vendredi 12 décembre 2014, 09h30 / Friday, December 12, 2014, 9:30 am

Amicable numbers

Résumé/Abstract : The concept goes back to Pythagoras: two numbers form an amicable pair if the sum of the proper divisors of one is the other, and vice versa. The study of the distribution of such numbers is more recent, going back about 60 years. In this lecture I will report on some very recent results on amicable numbers and related topics.

LIEU/VENUE
Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Salle / Room 6214

Jeudi 11 décembre 2014, 16h00 / Thursday, December 11, 2014, 4:00 pm

The first function

Résumé/Abstract: Let s(n) denote the sum of the positive divisors of n that are smaller than n. Introduced by Pythagoras 2500 years ago, it is perhaps the first function ever studied in mathematics. Steeped in numerology and colorful metaphors, the ancient problems associated with s(n) have led to much of number theory, including some very recent results.

LIEU/VENUE
Centre de recherches mathématiques
Pavillon Claire-McNicoll, Université de Montréal
Salle / Room Z-220

Une réception suivra la conférence au Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Salle 6245).
A reception will follow at the Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (Room 6245).