Displaying similar documents to “Generalizations of Midy's theorem on repeating decimals.”

Pocklington's Theorem and Bertrand's Postulate

Marco Riccardi (2006)

Formalized Mathematics

Similarity:

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.

Properties of Primes and Multiplicative Group of a Field

Kenichi Arai, Hiroyuki Okazaki (2009)

Formalized Mathematics

Similarity:

In the [16] has been proven that the multiplicative group Z/pZ* is a cyclic group. Likewise, finite subgroup of the multiplicative group of a field is a cyclic group. However, finite subgroup of the multiplicative group of a field being a cyclic group has not yet been proven. Therefore, it is of importance to prove that finite subgroup of the multiplicative group of a field is a cyclic group.Meanwhile, in cryptographic system like RSA, in which security basis depends upon the difficulty...

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

Andrzej Rotkiewicz (2005)

Acta Mathematica Universitatis Ostraviensis

Similarity:

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.