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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {1983},
     volume = {45},
     number = {2},
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     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/

[1] Mineev M. P., Pavlov A. I., “O chisle podstanovok spetsialnogo vida”, Matem. sb., 99 (141) (1976), 468–476 | MR | Zbl

[2] Pavlov A. I., “O chisle reshenii uravneniya $x^k=a$ v simmetricheskoi gruppe $S_n$”, Matem. sb., 112 (154) (1980), 380–395 | MR | Zbl