The explicit determination of perfect powers in (shifted) non-degenerate, integer, binary linear recurrence sequences has only been achieved in a handful of cases. In this talk, we combine bounds for linear forms in logarithms with results from the modularity of elliptic curves defined over totally real fields to explicitly determine all shifted powers by two in the Fibonacci sequence. This is joint work with Mike Bennett (UBC) and Samir Siksek (Warwick).
Zoom Meeting ID: 919 6497 4060
For password contact Pieter Moree (moree@mpim...).
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/246