BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katalin Gyarmati (Eötvös Loránd University) DTSTART:20261110T210000Z DTEND:20261110T220000Z DTSTAMP:20261019T005951Z UID:BinghamtonArithmeticSeminar/12 DESCRIPTION:Title: The Taxicab Problem for Polynomials and Generalizatio ns of Mason's Theorem\nby Katalin Gyarmati (Eötvös Loránd Universit y) as part of Binghamton Arithmetic Seminar\n\n\nAbstract\nThis talk is mo tivated by Ramanujan's famous taxicab problem and is concerned with the so lvability 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 the complex numbers. Usin g Wronskian determinants and Mason's theorem\, we obtain sharp upper bound s for the exponents. In particular\, we will show that there are no relati vely prime polynomials (with at least one non-constant) satisfying the gen eralised taxicab equation for $n \\ge 10$. We also consider an extension o f Mason's theorem to $f_0+f_1+\\dots+f_k=0$ for several polynomial terms o ver the complex numbers and finite fields\, obtaining the corresponding de gree bounds. Finally\, the talk points out interesting future cryptographi c applications of these theoretical results\, in particular\, the construc tion of large families of pseudorandom binary sequences with small cross-c orrelation measures.\n LOCATION:https://researchseminars.org/talk/BinghamtonArithmeticSeminar/12/ END:VEVENT END:VCALENDAR