On Friday, April 5, 2013 9:40:59 AM UTC+1, Paul wrote: > I'll admit up front that this post makes me definitely guilty of a near-repetition of something I posted earlier. This time, I think I have a clearer phrasing of what I want -- hence the repetition. > > > > Does anyone know of any real numbers r which have the following two properties? > > > > 1) r is known to be algebraic. > > 2) No one knows an explicit polynomial over Z for which r is a root. > > > > Hmmm.. > > I thought that was a really clear statement of what I'm trying to find. But it isn't because someone could say "r where r = the truth value (either 0 or 1) of the statement of the Goldbach conjecture." > > > > But that's not the type of thing I mean. I'm thinking of numbers which are given by an explicit series like eta(3). > > > > Thank You, > > > > Paul Epstein
It occurs to me that, in any case, my example of the type of answer I didn't want doesn't solve my problem, so it's unnecessary to give it as an example of an undesirable type of answer.
The Goldbach example doesn't satisfy (2) because that r is a root of x(x - 1) = 0.