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SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20260715T203000Z
DTEND:20260715T205500Z
DTSTAMP:20260805T044330Z
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 cyclotomic polynomials and either 
 a constant or an irreducible non-cyclotomic polynomial. Little progress ha
 s been made on this conjecture since then. In this talk\, I discuss 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 $\\Phi_{\\ell^{r} p}(x)+\\Phi_{\\ell^
 {r} q}(x)$ has this property and determine precisely the cyclotomic polyno
 mials dividing the sum.  We also discuss cases of the conjecture in which 
 the number of prime factors of $n$ and $m$ can be arbitrary.\n
LOCATION:https://researchseminars.org/talk/CANT2026/41/
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