One pile Nim with arbitrary move function.
Optimal bounds for the length of rational Collatz cycles
Partitioning the positive integers with higher order recurrences.
Perfect powers in linear recurring sequences
Period of a linear recurrence
Periodicity of Recurring Sequences in Rings.
Periodicity of some recurrence sequences modulo .
Permutations of the natural numbers with prescribed difference multisets.
Pisot Sequences.
Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire.
Polynomials of the form and pseudoprimes with respect to linear recurring sequences
Positivity of three-term recurrence sequences.
Power Sums of Integers with Missing Digits.
Power values of certain quadratic polynomials
In this article we compute the th power values of the quadratic polynomials with negative squarefree discriminant such that is coprime to the class number of the splitting field of over . The theory of unique factorisation and that of primitive divisors of integer sequences is used to deduce a bound on the values of which is small enough to allow the remaining cases to be easily checked. The results are used to determine all perfect power terms of certain polynomially generated integer...
PPCM de suites de polynômes
Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields
Let be a linear integer recurrent sequence of order , and define as the set of primes that divide at least one term of . We give a heuristic approach to the problem whether has a natural density, and prove that part of our heuristics is correct. Under the assumption of a generalization of Artin’s primitive root conjecture, we find that has positive lower density for “generic” sequences . Some numerical examples are included.
Primitive divisors of Lucas and Lehmer sequences, II
Let and are conjugate complex algebraic integers which generate Lucas or Lehmer sequences. We present an algorithm to search for elements of such sequences which have no primitive divisors. We use this algorithm to prove that for all and with h, the -th element of these sequences has a primitive divisor for . In the course of proving this result, we give an improvement of a result of Stewart concerning more general sequences.
Primitive prime factors in second-order linear recurrence sequences
Primzahlfragen in der Diophantischen Geometrie.
Propriétés algébriques de suites différentiellement finies