[seqfan] FLT-inspired sequence: what is known?

Valery Liskovets liskov at im.bas-net.by
Fri Mar 6 15:21:23 CET 2009

What is known about the sequence
  f(n)=min{|x^n+y^n-z^n|} over integers x,y,z>1?

Are there known values greater 1 and known n with f(n)=1?
Which initial values and non-trivial (i.e. better than 2^n)
upper bounds are known (apart from f(1)=f(2)=0, and
f(3)<3 since 5^3+6^3=7^3-2). Etc.

Valery Liskovets

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