Date: Jun 13, 1996 11:09 PM
Author: Stephen.Donnelly
Subject: How hard is this?



Hello all,

Here is a decision problem:

Given a (large) natural number N, a (small) natural number d
and bounds C and M, are there natural numbers m<M and c_i<C
(for each 0 \le i \le d) such that

N = c_d m^d + c_(d-1) m^(d-1) + ... + c_0 ?

In other words, is there a polynomial of degree d with co-
efficients less than C that takes value N at a point less
than M ?

(For example one might take M = C = O( N^(1/(d+1)) )

Does anyone know anything about the complexity of this or any
even vaguely similar problems?

Thanks,

Steve

donnelly@maths.anu.edu.au