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SUMMARY:The Fermat equation $x^13+y^13=3z^7$ [MPIM]
DTSTART:20250814T143000Z
DTEND:20250814T150000Z
DTSTAMP:20260815T093600Z
UID:indico-event-590@math-events.uni-bonn.de
DESCRIPTION:Speakers: Nuno Freitas (ICMAT\, Madrid/MPIM)\n\nNumber theory 
 lunch seminar\nThe modular method is a fantastic tool to solve families of
  Diophantineequations with a varying exponent\, but it often fails for sma
 ll values ofthe exponent. For example\, the Fermat-type equation $x^13+y^1
 3=3z^p$ has beensolved for all $p\\ne 7$. In this talk\, we will discuss h
 ow a combination of aunit sieve\, the modular method\, level raising and c
 omputations of systemsof eigenvalues modulo $7$\, and results for reducibi
 lity of certain Galoisrepresentations\, allows us to solve the missing cas
 e $p=7$.\n\nhttps://math-events.uni-bonn.de/event/590/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/590/
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