Perfect powers with all equal digits but one.
Perfect, Semiperfect and Ore Numbers
Periodic expansions and units in quadratic and cubic number fields.
Periodic Jacobi-Perron expansions associated with a unit
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.
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.