Displaying similar documents to “A generalization of a necessary and sufficient condition for primality due to Vantieghem.”

Leudesdorf's theorem and Bernoulli numbers

I. Sh. Slavutsky (1999)

Archivum Mathematicum

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For m ∈ , ( m , 6 ) = 1 , it is proved the relations between the sums W ( m , s ) = ∑ i = 1 , ( i , m ) = 1 m - 1 i - s , s ∈ , 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.

On pseudoprimes having special forms and a solution of K. Szymiczek’s problem

Andrzej Rotkiewicz (2005)

Acta Mathematica Universitatis Ostraviensis

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We use the properties of p -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.

Pocklington's Theorem and Bertrand's Postulate

Marco Riccardi (2006)

Formalized Mathematics

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The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.