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**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 (a_{n}) of integers such that the set of primes p, for which p|a_{n} 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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