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SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20260715T203000Z
DTEND:20260715T205500Z
DTSTAMP:20260710T111454Z
UID:CANT2026/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/41/
 ">On the factorization of a sum of cyclotomic polynomials</a>\nby Michael 
 Filaseta (University of South Carolina) 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\nIn 2000\, Charles Nico
 l conjectured that for $n$ and $m$ integers with $n > m >1$\, the sum $\\P
 hi_{n}(x)+\\Phi_{m}(x)$ is a product of distinct cyclotomic polynomials an
 d either a constant or an irreducible non-cyclotomic polynomial. Little pr
 ogress has been made on this conjecture since then. In this talk\, we disc
 uss recent joint work with Lilit Martirosyan and London Swan\, where\, in 
 particular\, we show that for primes $p$\, $q$ and $\\ell$ with $p > q > \
 \ell$ and a non-negative integer $r$\, the sum $\\Phi_{\\ell^{r} p}(x)+\\P
 hi_{\\ell^{r} q}(x)$ has this property and determine precisely the cycloto
 mic polynomials dividing the sum.\n
LOCATION:https://researchseminars.org/talk/CANT2026/41/
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