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)-1i = 1(ui+1-ui)\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 = u1 < u2 < ... < 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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