Periodic, Multiplicative Number-Theoretical Functions.
Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function
Periodicity of p-adic continued fractions.
Periodische und multiplikative zahlentheoretische Funktionen.
Periodizitätseigenschaften p-adischer Kettenbrüche.
Periods of β-expansions and linear recurrent sequences
Petites solutions des congruences
Piatetski-Shapiro sequences via Beatty sequences
Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with asymptotic...
Picturesque exponential sums. II:
Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire.
Pm numbers, ambiguity, and regularity
Poly-Bernoulli numbers
By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.
Polylogarithms and arithmetic function spaces
Polynomial continued fractions
Polynomial extension of Fleck's congruence
Polynomials Involving the Floor Function.
Polynomials of Pellian Type and Continued Fractions
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex-...
Portraits of Numbers
Positive integers such that .
Positive integers such that .