On the density of some sets of primes \(p\), for which \((\text{ord}_ p b,n)=d\) (Q685256)

For any prime \(p\) and integer \(b>1\) coprime to \(p\) let \(\text{ord}_ p b\) denote the least positive integer \(r\) such that \(b^ r\equiv 1\bmod p\). In an earlier paper [Acta Arith. 43, 177-190 (1984; Zbl 0531.10049)] the author obtained an asymptotic formula with logarithmic error term for the number of primes \(p\leq x\) such that \((\text{ord}_ p b,n)=1\), where \(b>1\) and \(n>1\) are given integers. In the paper under review, he generalizes this result to the counting function of primes \(p\) satisfying \((\text{ord}_ p b,n)=d\), for some given divisor \(d\) of \(n\).