BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katalin Gyarmati (Eötvös Loránd University\, Hungary) DTSTART:20260717T183000Z DTEND:20260717T185500Z DTSTAMP:20260710T111654Z UID:CANT2026/70 DESCRIPTION:Title: The taxicab problem for polynomials and generalizations of Mason’s the orem\nby Katalin Gyarmati (Eötvös Loránd University\, Hungary) as p art of Combinatorial and additive number theory seminar (CANT 2026)\n\nLec ture held in Science Center in the CUNY Graduate Center (4th floor).\n\nAb stract\nThis talk is motivated by Ramanujan's famous taxicab problem and i s concerned with the solvability of polynomial equations of the form $p^n+ q^n=r^n+s^n$ and\, more generally\, $p_1^{k_1}+\\dots+p_m^{k_m}=0$ over th e complex numbers. Using Wronskian determinants and Mason's theorem\, we o btain sharp upper bounds for the exponents. In particular\, we will show t hat there are no relatively prime polynomials (with at least one non-const ant) satisfying the generalised taxicab equation for $n \\ge 16$. We also consider an extension of Mason's theorem to $f_0+f_1+\\dots+f_k=0$ for sev eral polynomial terms over the complex numbers and finite fields\, obtaini ng the corresponding degree bounds. Finally\, the talk points out interes ting future cryptographic applications of these theoretical results\, in p articular\, the construction of large families of pseudorandom binary sequ ences with small cross-correlation measures.\n LOCATION:https://researchseminars.org/talk/CANT2026/70/ END:VEVENT END:VCALENDAR