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SUMMARY:Multiplicative properties of sumsets and multiplicative properties
  of shifted sets\n - Christian Elsholtz\, Royal Holloway
DTSTART:20080219T160000Z
DTEND:20080219T170000Z
UID:TALK9062@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:In this talk we will study how large sets A and B of integers 
 can be \nif all elements of their sumset A+B are supposed to have a\nspeci
 fied multiplicative form. We also sudy the related problem\nwhere shifted 
 elements of product sets have a specified multiplicative\nform.\n\nExample
 s:\n1) An open problem of Ostmann states that there are no two sets of\nin
 tegers A and B\, with at least two elements each such that A+B is\n(apart 
 from finitely many elements) the set of primes.\n\nThis problem is related
  to the twin prime problem.\nLet A={0\,2}. Is there an infinite set B such
  that A+B is a subset of the\nprimes? \n\n2) In contrast\, the sumset of t
 he set of squares satisfies a\nmultiplicative constraint.\n3) We also look
  at shifted copies of product sets and study for example\nif the set of sh
 ifted primes P-1 can be multiplicatively decomposed.\n\nThis is related to
  another famous problem:\nLet A={6\,12\,18}. Is there an infinite set B su
 ch that AB+1 is a subset\nof the primes? This would imply there are infini
 tely many Carmichael\nnumbers with 3 prime factors.\n
LOCATION:MR4\, CMS
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