Geodesic
On the limit distribution of the number of solutions of the equation $x^k=a$ in the symmetric group $S_n$
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 243-255

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The limit distribution of the number of solutions of the equation $x^k=a$ as $n\to\infty$ is investigated for a fixed integer $k\geqslant2$, where $a$ is in the symmetric group $S_n$ of degree $n$. Bibliography: 2 titles. 
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     author = {A. I. Pavlov},
     title = {On the limit distribution of the number of solutions of the equation $x^k=a$ in the symmetric group $S_n$},
     journal = {Sbornik. Mathematics},
     pages = {243--255},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_2_a5/}
}
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A. I. Pavlov. On the limit distribution of the number of solutions of the equation $x^k=a$ in the symmetric group $S_n$. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 243-255. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a5/