A newer extreme abc-example due to Tim Dokchitser
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Tim Dokchitser just wrote a paper "LLL & ABC" in which he presents
(apart from developing a new interesting method for abc-hunting)
a new record for the uniform abc-conjecture.
Let r = (3+sqrt(13))/2. Then
r^-5 (r-1) + r^5 (r-2) = 2^9
has quality 2.02922...
My congratulations to Tim!
It's not hard to see that this example is related to
2^16 - 13 71^2 = -3.
August 2003,
Benne de Weger