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SUMMARY:Eric Delaygue (University Lyon 1)
DTSTART:20210524T111500Z
DTEND:20210524T121500Z
DTSTAMP:20260423T022921Z
UID:WarsawNT/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/32/
 ">On primary pseudo-polynomials and around Ruzsa's Conjecture</a>\nby Eric
  Delaygue (University Lyon 1) as part of Warsaw Number Theory Seminar\n\nL
 ecture held in currently online.\n\nAbstract\nEvery polynomial $P(X)$ with
  integer coefficients satisfies the congruences $P(n+m)=P(n) \\mod m$ for 
 all integers $n$ and $m$. An integer valued sequence is called a pseudo-po
 lynomial when it satisfies these congruences. Hall characterized pseudo-po
 lynomials and proved that they are not necessarily polynomials. A long sta
 nding conjecture of Ruzsa says that a pseudo-polynomial $a(n)$ is a polyno
 mial as soon as $\\limsup |a_n|^{1/n} < e$. A primary pseudo-polynomial is
  an integer valued sequence $a(n)$ such that $a(n+p)=a(n) \\mod p$ for all
  integers $n ≥ 0$ and all prime numbers $p$. The same conjecture has bee
 n formulated for them\, which implies Ruzsa’s\, and this talk will revol
 ve around this conjecture.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/32/
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