On a conjecture of Graham on the p-divisibility of central binomial coefficients

Series
Combinatorics Seminar
Time
Friday, September 16, 2022 - 3:00pm for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Ernie Croot – Georgia Institute of Technology – https://ecroot.math.gatech.edu/
Organizer

I will discuss an old conjecture of Ron Graham on whether there are infinitely many integers $n$ so that $\mathrm{gcd}({{2n} \choose n}, 105)=1$, as well as recent progress on a version of this problem where 105 is replaced with a product of $r$ distinct primes. This is joint work with Hamed Mousavi and Maxie Schmidt.