Zeros Prime Capacity of Monic Polynomials Using Integer Coefficients

Illustrations of Congruences and Sums of Zeros in Monic Polynomials

Abstract

Fora monic polynomial with integer coefficients the sum Sk of the kth powersof the zeros is an integer, for positive integer k. For prime p,  (modp); and hence, if ax - 0 then  thensimilar congruences hold for sums of negative powers of the zeros.Illustrations are given for various types of Chebyshev polynomials with integerargument.