Geodesic
Leudesdorf's theorem and Bernoulli numbers
Archivum mathematicum, Tome 35 (1999) no. 4, pp. 299-303 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For $m\in $, $(m,6)=1$, it is proved the relations between the sums \[ W(m,s)=\sum _{i=1, (i,m)=1}^{m-1} i^{-s}\,, \quad \quad s\in \,, \] and Bernoulli numbers. The result supplements the known theorems of C. Leudesdorf, N. Rama Rao and others. As the application it is obtained some connections between the sums $W(m,s)$ and Agoh’s functions, Wilson quotients, the indices irregularity of Bernoulli numbers.
For $m\in $, $(m,6)=1$, it is proved the relations between the sums \[ W(m,s)=\sum _{i=1, (i,m)=1}^{m-1} i^{-s}\,, \quad \quad s\in \,, \] and Bernoulli numbers. The result supplements the known theorems of C. Leudesdorf, N. Rama Rao and others. As the application it is obtained some connections between the sums $W(m,s)$ and Agoh’s functions, Wilson quotients, the indices irregularity of Bernoulli numbers.
Classification : 11A07, 11B68
Keywords: Wolstenholme-Leudesdorf theorem; p-integer number; Bernoulli number; Wilson quotient; irregular prime number 
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     author = {Slavutskii, I. Sh.},
     title = {Leudesdorf's theorem and {Bernoulli} numbers},
     journal = {Archivum mathematicum},
     pages = {299--303},
     year = {1999},
     volume = {35},
     number = {4},
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     zbl = {1053.11003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999_35_4_a1/}
}
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Slavutskii, I. Sh. Leudesdorf's theorem and Bernoulli numbers. Archivum mathematicum, Tome 35 (1999) no. 4, pp. 299-303. http://geodesic.mathdoc.fr/item/ARM_1999_35_4_a1/