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SUMMARY:The minimum modulus of a covering system is at most 10^19 - Bob Ho
 ugh (University of Cambridge)
DTSTART:20131205T143000Z
DTEND:20131205T153000Z
UID:TALK48120@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Abstract: A distinct covering system of congruences is a colle
 ction\n\na_i mod m_i\,  1 < m_1 < m_2 < ... < m_k\n\nsuch that every integ
 er satisfies at least one of them. Erd\\H{o}s asked whether there exist co
 vering systems for which m_1 is arbitrarily large. I have recently found a
  negative answer to this question. I will describe\naspects of the proof\,
  which uses in a crucial way a relative form of the Lov\\'asz Local Lemma.
 \n
LOCATION:MR12
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