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SUMMARY:Ivan V. Morozov (City College (CUNY))
DTSTART:20260715T140000Z
DTEND:20260715T142500Z
DTSTAMP:20260710T111453Z
UID:CANT2026/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/33/
 ">On quotients of a more general theorem of Wilson</a>\nby Ivan V. Morozov
  (City College (CUNY)) as part of Combinatorial and additive number theory
  seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduat
 e Center (4th floor).\n\nAbstract\nThe basis of this work is a corollary a
 nd generalization of Wilson’s theorem\, $(-1)^{k}k!(n-k-1)!\\equiv -1\\p
 mod{n}$ iff $n$ is non-composite\, for $0\\leq k\\leq n-1$. This corollary
  generates many more quotients than those already generated by Wilson’s 
 theorem\, and we derive how they relate to each other and build on the est
 ablished properties of the original quotients. The main results are expres
 sions for sums of these quotients\, modular congruences that extend the re
 sults of Lehmer\, and generating functions. In addition\, a solution will 
 be provided for an open problem raised in CANT 2025 by Brian Hopkins regar
 ding a combinatorial proof for the partition identity $p(a\,3)+p(b\,3)=p(c
 \,3)$\, where $a$\, $b$\, and $c$ comprise a Pythgagorean triple.\n
LOCATION:https://researchseminars.org/talk/CANT2026/33/
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