Abstract
We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. The second result has application to polynomial GCD computation and solving polynomial diophantine equations.
Highlights
Let Fq denote the finite field with q elements and let Zn denote the ring of integers modulo n
Let f be a polynomial in Fq[x] of a given degree d > 0 and let X be the number of distinct roots of f
The two main results presented in this paper are Theorems 1 and 2 below
Summary
Let Fq denote the finite field with q elements and let Zn denote the ring of integers modulo n. Let X be a random variable which counts the number of distinct roots of a monic polynomial in Zn[x] of degree m > 0.
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