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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 515.10002

**Autor: ** Erdös, Paul

**Title: ** Many old and on some new problems of mine in number theory. (In English)

**Source: ** Numerical mathematics and computing, Proc. 10th Manitoba Conf., Winnipeg/Manitoba 1980, Congr. Numerantium 30, 3-27 (1981).

**Review: ** [This article was published in the book announced in Zbl 504.00026.]

The author has been keeping a mathematical notebook since 1933. The present paper consists of a long list of theorems, problems, conjectures and questions gleaned from this notebook. It is divided into three parts: problems on primes, problems on consecutive integers, and a potpourri of miscellaneous problems. I will mention just a few of these problems. Let p_{1} < p_{2} < ... be an infinite sequence of primes such that p_{k}\equiv 1(mod p_{k-1}). Is it true that p_{k}^{1/k} ––> oo? Let **prod**(n,k) = (n+1)...(n+k) where k > 2. Is there always a prime p \geq k such that p|**prod**(n,k)? Let f(n) be the smallest integer such that one can partition the integers 1,2,3,...,n-1 into f(n) classes so that n is not the sum of distinct integers of the same class. How fast does f(n) tend to infinity? I am sure that Professor Erdös would be glad to hear from anyone who can shed some light on any (or all) of these questions.

**Reviewer: ** P.Hagis

**Classif.: ** * 11-02 Research monographs (number theory)

11N05 Distribution of primes

00A07 Problem books

**Keywords: ** problems on primes; problems on consecutive integers; miscellaneous problems

**Citations: ** Zbl.504.00026

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