Hagedorn, Thomas R.; Hatley, Jeffrey The probability of relatively prime polynomials in \(\mathbb Z_{p^k}[x]\). (English) Zbl 1219.11050 Involve 3, No. 2, 223-232 (2010). Let \(P_R(m,n)\) be the probability that two monic polynomials of degrees \(m\) and \(n\), randomly chosen in \(R[x]\), are relatively prime. For the finite field \(R={\mathbb F}_q\), we have \(P_R(m,n)=1-q^{-1}\) for all \(m,n\geq1\). In this paper, the authors study the probability for the ring \(R={\mathbb Z}_q\) of integers modulo \(q\) and give an explicit formula for \(P_R(m,2)\) where \(q\) is an odd prime power. Reviewer: Astrid Reifegerste (Magdeburg) Cited in 1 Document MSC: 11C20 Matrices, determinants in number theory 13B25 Polynomials over commutative rings 13F20 Polynomial rings and ideals; rings of integer-valued polynomials Keywords:polynomials over integers modulo q; relative prime polynomials PDFBibTeX XMLCite \textit{T. R. Hagedorn} and \textit{J. Hatley}, Involve 3, No. 2, 223--232 (2010; Zbl 1219.11050) Full Text: DOI Link