lost a Mathematica 7.0 that had gone 2.5 days on
Factor[x^3-3^(3/5)+2^(1/5), Extension -> {5^(1/3),2^(1/5),3^(1/5)}]
MReid> its linear factor should be
x - (3^(1/5) + 4^(1/5) - 54^(1/5) + 72^(1/5))/5^(2/3)
and of course the quadratic cofactor is irreducible.
mike
Thereby reenacting one of my favorite denestings: 1/5 3/5 3/5 2/5 1/5 2/5 3/5 1/5 1/3 - 2 3 + 2 3 + 3 + 2 (3 - 2 ) = ------------------------------------- , 2/3 5 a major simplification that looks anything but. For greater intrigue, I have numerous cases of sqrt(binomial) = pentanomial, but *never* anything higher, except complex. Are there any real ones?? --rwg NTH ROOT SHORT TON LOCUST BEAN UNCOUNTABLES