Resumen de Detecting prime numbers via roots of polynomials

David E. Dobbs

• It is proved that an integer n?=?2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial fwith coefficients in Zn, the ring of integers modulo n, such that each element of Znis a root of f. This classroom note could find use in any introductory course on abstract algebra or elementary number theory.