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SUMMARY:Alexander Kalmynim (Higher School of Economics\, Russia)
DTSTART:20260717T143000Z
DTEND:20260717T145500Z
DTSTAMP:20260710T111703Z
UID:CANT2026/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/62/
 ">Sárközy’s conjecture on quadratic residues</a>\nby Alexander Kalmyni
 m (Higher School of Economics\, Russia) as part of Combinatorial and addit
 ive number theory seminar (CANT 2026)\n\nLecture held in Science Center in
  the CUNY Graduate Center (4th floor).\n\nAbstract\nFor an odd prime numbe
 r $p$\, let $\\mathcal R_p\\subset \\mathbb F_p$ be the set of all non-zer
 o quadratic residues. A. Sárközy conjectured that the set $\\mathcal R_p
 $ does not admit a non-trivial additive decomposition for large enough $p$
 \, i.e. for $p>p_0$ the identity $A+B=\\mathcal R_p$ implies $\\min(|A|\,|
 B|)=1$. In this talk we present a complete resolution of Sárközy's conje
 cture. Further\, we show that\, for a subgroup $G\\subset \\mathbb F_p^*$\
 , the equality $G\\cup\\{0\\}=A-A$ for some $A$ implies $|G|=2$ or $6$ and
  if $G=A+B$ non-trivially\, then $|A|=|B|=\\sqrt{|G|}$.\n
LOCATION:https://researchseminars.org/talk/CANT2026/62/
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