Seminar series
Date
Thu, 13 Feb 2014
Time
16:00 -
17:00
Location
L5
Speaker
Bob Hough
Organisation
Oxford University
A distinct covering system of congruences is a collection
\[
(a_i \bmod m_i), \qquad 1\ \textless\ m_1\ \textless\ m_2\ \textless\ \ldots\ \textless\ m_k
\]
whose union is the integers. Erd\"os asked whether there are covering systems for which $m_1$ is arbitrarily large. I will describe my negative answer to this problem, which involves the Lov\'{a}sz Local Lemma and the theory of smooth numbers.