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DTSTART:20190310T070000
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DTSTART;TZID=America/Toronto:20190326T123000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-71
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:VANDITA PATEL\, UNIVERSITY OF TORONTO\n\n\"A Galois property of
  even degree Bernoulli polynomials\"\n\nLet $k$ be an even integer such th
 at $k$ is at least $2$. We give a\n(natural) density result to show that f
 or 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 solutions $(x\,y\,n
 )$. The proof relies upon\nsome Galois theory and group theory\, whereby w
 e deduce\nsome interesting properties of the Bernoulli polynomials. This 
 is\njoint work with Samir Siksek (University of Warwick).\n\nMC 5417
DTSTAMP:20260606T154256Z
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