BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Solaleh Bolvardizadeh (University of Lethbridge)
DTSTART:20221121T190000Z
DTEND:20221121T200000Z
DTSTAMP:20260404T151817Z
UID:NTC/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NTC/9
 /">On the Quality of the $ABC$-Solutions</a>\nby Solaleh Bolvardizadeh (Un
 iversity of Lethbridge) as part of Lethbridge number theory and combinator
 ics seminar\n\nLecture held in University of Lethbridge: M1040 (Markin Hal
 l).\n\nAbstract\nThe quality of the triplet $(a\,b\,c)$\, where $\\gcd(a\,
 b\,c) = 1$\, satisfying $a + b = c$ is defined as\n$$\nq(a\,b\,c) = \\frac
 {\\max\\{\\log |a|\, \\log |b|\, \\log |c|\\}}{\\log \\mathrm{rad}(|abc|)}
 \,\n$$\nwhere $\\mathrm{rad}(|abc|)$ is the product of distinct prime fact
 ors of $|abc|$. We call such a triplet an $ABC$-solution. The $ABC$-conjec
 ture states that given $\\epsilon > 0$ the number of the $ABC$-solutions $
 (a\,b\,c)$ with $q(a\,b\,c) \\geq 1 + \\epsilon$ is finite.\n\nIn the firs
 t part of this talk\, under the $ABC$-conjecture\, we explore the quality 
 of certain families of the $ABC$-solutions formed by terms in Lucas and as
 sociated Lucas sequences. We also introduce\, unconditionally\, a new fami
 ly of $ABC$-solutions that has quality $> 1$.\n\nIn the remaining of the t
 alk\, we prove a conjecture of Erd\\"os on the solutions of the Brocard-Ra
 manujan equation\n$$\nn! + 1 = m^2\n$$\nby assuming an explicit version of
  the $ABC$-conjecture proposed by Baker.\n
LOCATION:https://stable.researchseminars.org/talk/NTC/9/
END:VEVENT
END:VCALENDAR