19 Mar
2006
19 Mar
'06
4:50 p.m.
Assuming Dan means the set of images as the polynomial and its degree take (dome?) all possible values, my distant and foggy memory claims it's the recursively enumerable sets, by Matasevic's theorem --- I think n = 26 suffices. Having recently been sat upon for my poor historical research, I have just attempted to verify this on Google --- but oddly can raise not a single hit. Any logicians out there? 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