Well, if someone shows you an x0 such that f(x0)=0, then the verification is trivial; finding that x0 might have taken eons, but once it has been found, it is easily verified. So the intermediate value theorem is still an example for you. At 08:55 AM 11/15/2011, Marc LeBrun wrote:
="Henry Baker" <hbaker1@pipeline.com> Aren't most proofs of the "intermediate value theorem" essentially non-constructive?
I again apologize for not being clear what I was asking for--I buried the second half of the conjunction too deeply in the prose:
=Marc LeBrun ... a non-constructive proof... that ALSO has an easily-verified case?
Come to think of it factoring provides an example: you can easily and non-constructively show that some big N is composite, AND you can easily verify that some X divides N, BUT finding X is hard.
Thanks for all the suggestions!