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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Multiplicative properties of sumsets and multiplic
ative properties of shifted sets\n - Christian Els
holtz\, Royal Holloway
DTSTART;TZID=Europe/London:20080219T160000
DTEND;TZID=Europe/London:20080219T170000
UID:TALK9062AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/9062
DESCRIPTION:In this talk we will study how large sets A and B
of integers can be \nif all elements of their sums
et A+B are supposed to have a\nspecified multiplic
ative form. We also sudy the related problem\nwher
e shifted elements of product sets have a specifie
d multiplicative\nform.\n\nExamples:\n1) An open p
roblem of Ostmann states that there are no two set
s of\nintegers A and B\, with at least two element
s each such that A+B is\n(apart from finitely many
elements) the set of primes.\n\nThis problem is r
elated to the twin prime problem.\nLet A={0\,2}. I
s there an infinite set B such that A+B is a subse
t of the\nprimes? \n\n2) In contrast\, the sumset
of the 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
shifted primes P-1 can be multiplicatively decompo
sed.\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 woul
d imply there are infinitely many Carmichael\nnumb
ers with 3 prime factors.\n
LOCATION:MR4\, CMS
CONTACT:Ben Green
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