Found it --- spelling Matyasevic or Matijasevic. E.g. there is a 2006 page at http://primes.utm.edu/glossary/page.php?sort=MatijasevicPoly giving the 26 variable generator I was thinking about --- which unhappily only generates primes, and only as its positive values. I haven't seen the 1971 paper referred to there, but I guess it shows that any r.e. set can be generated as the positive values of a polynomial. The page also mentions that there is no polynomial which generates the primes, so Dan's question is evidently still open. Fred Lunnon On 3/19/06, dasimov@earthlink.net <dasimov@earthlink.net> wrote:
... Given a polynomial function of degree d, in n variables, with integer coefficients
P: Z^n -> Z,
characterize the set I(n,d) of all possible images.
(I don't know whether this problem has been solved or not. Anyone know if it has?)
--Dan
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