Displaying similar documents to “Integer sequences and periodic points.”

Counting monic irreducible polynomials P in 𝔽 q [ X ] for which order of X ( mod P ) is odd

Christian Ballot (2007)

Journal de Théorie des Nombres de Bordeaux

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Hasse showed the existence and computed the Dirichlet density of the set of primes p for which the order of 2 ( mod p ) is odd; it is 7 / 24 . Here we mimic successfully Hasse’s method to compute the density δ q of monic irreducibles P in 𝔽 q [ X ] for which the order of X ( mod P ) is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the δ p ’s as p varies through all rational primes.

More on Divisibility Criteria for Selected Primes

Adam Naumowicz, Radosław Piliszek (2013)

Formalized Mathematics

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This paper is a continuation of [19], where the divisibility criteria for initial prime numbers based on their representation in the decimal system were formalized. In the current paper we consider all primes up to 101 to demonstrate the method presented in [7].