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University of Cambridge > Talks.cam > Combinatorics Seminar > The minimum modulus of a covering system is at most 10^19

## The minimum modulus of a covering system is at most 10^19Add to your list(s) Download to your calendar using vCal - Bob Hough (University of Cambridge)
- Thursday 05 December 2013, 14:30-15:30
- MR12.
If you have a question about this talk, please contact Andrew Thomason. Abstract: A distinct covering system of congruences is a collection a_i mod m_i, 1 < m_1 < m_2 < ... < m_k such that every integer satisfies at least one of them. Erd\H{o}s asked whether there exist covering systems for which m_1 is arbitrarily large. I have recently found a negative answer to this question. I will describe aspects of the proof, which uses in a crucial way a relative form of the Lov\’asz Local Lemma. This talk is part of the Combinatorics Seminar series. ## This talk is included in these lists:- All CMS events
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