Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  709.11015
Autor:  Erdös, Paul; Maxsein, Th.; Smith, P.R.
Title:  Primzahlpotenzen in rekurrenten Folgen. (Prime powers in recurrent sequences.) (In German)
Source:  Analysis 10, No.1, 71-83 (1990).
Review:  Authors' abstract: We determine the structure of recurrent sequences of natural numbers which consist only of primes or prime powers. For example it is shown that a recurrent sequence of primes must be periodic. In order to obtain the results, the theorem of Mahler-Lech is used to bound the number of distinct infinite multiplicity values taken by a recurrent sequence of complex numbers. Further we employ a theorem of Pólya about recurrent sequences (an) of integers such that the set of primes p, for which p|an for some n, is finite.
Reviewer:  P.Kiss
Classif.:  * 11B37 Recurrences
                   30B40 Analytic continuation (one complex variable)
Keywords:  power series; recurrent sequences; primes; prime powers

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