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SUMMARY:Lajos Hajdu (University of Debrecen)
DTSTART:20200602T143000Z
DTEND:20200602T145500Z
DTSTAMP:20260423T011238Z
UID:CANT2020/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/18/
 ">Skolem's conjecture for a family of exponential equations</a>\nby Lajos 
 Hajdu (University of Debrecen) as part of Combinatorial and additive numbe
 r theory (CANT 2021)\n\n\nAbstract\nAccording to Skolem's conjecture\, if 
 an exponential Diophantine equation is not solvable\, \nthen it is not sol
 vable modulo an appropriately chosen modulus. Besides several concrete \ne
 quations\, the conjecture has only been proved for rather special cases. \
 nIn the talk we present a new theorem proving the conjecture for equations
  of the form \n$x^n-by_1^{k_1}\\dots y_\\ell^{k_\\ell}=\\pm 1$\, where $b\
 ,x\,y_1\,\\dots\,y_\\ell$ are fixed integers \nand $n\,k_1\,\\dots\,k_\\el
 l$ are non-negative integral unknowns. Note that the family includes \nthe
  famous equations $x^n-y^k=1$ and $\\frac{x^n-1}{x-1}=y^k$ with $x\,y$ fix
 ed. \n\nJoint with A. Bérczes and R. Tijdeman.\n
LOCATION:https://researchseminars.org/talk/CANT2020/18/
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