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DTSTART:20190310T070000
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URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/galois-prope
 rty-even-degree-bernoulli-polynomials
SUMMARY:A Galois property of even degree Bernoulli polynomials
CLASS:PUBLIC
DESCRIPTION:VANDITA PATEL\, UNIVERSITY OF TORONTO\n\nLet $k$ be an even int
 eger such that $k$ is at least $2$. We give a\n(natural) density result to
  show that for almost all $d$ at least $2$\,\nthe equation $(x+1)^k + (x+2
 )^k + ... + (x+d)^k = y^n$ with $n$ at\nleast $2$\, has no integer solutio
 ns $(x\,y\,n)$. The proof relies upon\nsome Galois theory and group theory
 \, whereby we deduce some\ninteresting properties of the Bernoulli polynom
 ials. This is joint\nwork with Samir Siksek (University of Warwick).\n\nMC
  5417
DTSTAMP:20260311T152237Z
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