The main goal of this paper is to show that the problem of finding approximately a zero of a polynomial system of equations can be solved in polynomial time, on the average. The number of arithmetic operations is bounded by cN4, where N is the number of input variables and c is a universal constant. Let us be more precise. For d = (d 1, . . . , d,) each di a positive integer, let ZCd, be the li...

We investigate the linear complexity and the minimal polynomial over the finite fields of the characteristic sequences of cubic and biquadratic residue classes. Also we find the linear complexity and the minimal polynomial of the balanced cyclotomic sequences of order three. Keywords—linear complexity, finite field, cubic residue classes, biquadratic residue classes