Student Colloquium

Samin Riasat, Department of Pure Mathematics, University of Waterloo

“The least prime factor of a binomial coefficient”

A conjecture of Erdo ̋s and Selfridge states that if n and k are positive integers with n > k2, then the binomial coefficient has a prime factor not exceeding n/k, with the unique exception of k6 We provide sufficient conditions under which the conjecture is true. In particular, we show that the conjecture holds when n ≥ lcm(1,2,...,k) + k − 1. What does this mean for k = 6? Lastly, if time permits, we shall briefly discuss why the bound n/k is expected to be the best possible.

QNC 1507