Thanks Douglas, that's a nice trick. +1 My method (basically weak approximation) extends to obtaining any even number of non-real roots.

Frank Adams's book "Algebraic topology: a student's guide" is a collection of such classic papers.

Hello Franz. At one stage I hoped that Fekete polynomials would help with my "evil determinant" problem (see my website) but I couldn't make them do so.

Kevin: I only noticed this recently when pondering Miles Reid's comments included in the errata for the second edition of Silverman's Arithmetic of Elliptic Curves.

Meadows (as defined by Bergstra et al) are essentially the same as commutative von Neumann regular rings: en.wikipedia.org/wiki/Von_Neumann_regular_ring .

Thomassen's paper can be downloaded from Andrew Ranicki's website at maths.ed.ac.uk/~aar/jordan/index.htm . I think there's a fixable error in his main proof. He assumes that if a point is accessible from a region, then after one puts in a polygonal path based at the point then it is still accessible from the new regions. This is false: consider the "cuspidal cubic" curve. But one can retrieve the situation by redfining accessibility by insisting that a positive angle's worth of segments starting at the given point and going into the given region.