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**Zentralblatt MATH**

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

**Zbl.No: ** 581.10019

**Autor: ** Erdös, Paul

**Title: ** Problems and results on consecutive integers and prime factors of binomial coefficients. (In English)

**Source: ** Rocky Mt. J. Math. 15, 358-363 (1985).

**Review: ** The author lists a number of interesting problems on consecutive integers and prime factors of binomial coefficients. He outlines the progress on these problems. Quite a few of the progress on these problems is due to the author. Also the author has encouraged the progress of work on these and many other problems. For example the ({$} 500) problem (1/\phi (n))**sum**^{\phi (n)-1}_{i = 1}(u_{i+1}-u_{i})^{\alpha} << (n/\phi (n))^{\alpha} for \alpha = 2 proposed by the author has been solved recently in fact for \alpha \geq 2 by H. L. Montgomery and R. C. Vaughan. Here n \geq 3, 1 = u_{1} < u_{2} < ... < u_{\phi (n)} = n-1 are the integers less than and coprime to n.

**Reviewer: ** K.Ramachandra

**Classif.: ** * 11N37 Asymptotic results on arithmetic functions

11-02 Research monographs (number theory)

00A07 Problem books

**Keywords: ** problems; consecutive integers; prime factors of binomial coefficients

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