The minimum modulus of a covering system is at most 10^19

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• 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.

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