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How hard is this?
Posted:
Jun 13, 1996 11:09 PM


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_(d1) m^(d1) + ... + 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



