The probability of relatively prime polynomials in \(\mathbb Z_{p^k}[x]\)
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.
scientific article; zbMATH DE number 5781534