ON THE NUMBER OF SOLUTIONS OF THE EQUATION $x^k = a$ IN THE SYMMETRIC GROUP $S_n$
Alexander Ivanovich Pavlov · Mathematics of the USSR-Sbornik · 1981
This paper consists of three sections. In the first a formula is given for the number of solutions of the equation in depending on the cyclic structure of the permutation . In the second an asymptotic formula is given for the quantity for a fixed as . In the third an asymptotic formula is found for the cardinality of the set of permutations such that the equation has a unique solution. Bibliography: 5 titles.