Publications of (and about) Paul Erdös
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 p1 < p2 < ... be an infinite sequence of primes such that pk\equiv 1(mod pk-1). Is it true that pk1/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.
Classif.: * 11-02 Research monographs (number theory)
11N05 Distribution of primes
00A07 Problem books
Keywords: problems on primes; problems on consecutive integers; miscellaneous problems
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