|Math Coffee: "Odd Perfect Numbers" Dr. Kevin Hare, University of Waterloo
When: April 16,
Speaker: Dr. Kevin Hare, University of WaterlooTicket Required: No
A perfect number N is a number such that the sum of the proper divisors of N is equal to N. The first two examples are 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14. The study of perfect numbers, and their properties has a long history, starting with Euclid (330?--275? B.C.) and going up to modern time.
Despite this long history, there are still a number of open questions concerning perfect numbers. Probably the oldest is, are any of them odd. (Currently only even perfect numbers are known.)
With the help of modern computers, a number of results concerning the non-existence of odd perfect numbers have been given. Some examples are
• If an odd perfect number exists, it is bigger than 10^300.
• If an odd perfect number exists, it has more than 75 prime factors.
• If an odd perfect number exists, it has a prime factor greater than 10^8.
In this talk, we will talk both about the history of perfect numbers, as well as some of the computational challenges involved in proving results about perfect numbers.
We will gather after the talk at about 3:30 in Math Hall for light snacks.
Contact: Prof. Donna Molinek