Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  354.10010
Autor:  Erdös, Paul; Graham, Ronald L.
Title:  On the prime factors of \binom{n}{k}. (In English)
Source:  Fibonacci Q. 14, 348-352 (1976).
Review:  Let \binom{n}{k} = un(k)vn(k), where un(k) contains the prime factors p < k and vk(n) those \geq k. Results:
I. max1 \leq k \leq nvn(k) = \exp(n/2+o(n)).
II. un(k) > 1 for some k \leq (2+o(1)) log n.
III. The value of k for which un(k) is maximal satisfies k = (1+o(1))(e/e+1)n.
Reviewer:  I.Z.Ruzsa
Classif.:  * 11B39 Special numbers, etc.
                   05A10 Combinatorial functions
                   11A41 Elemementary prime number theory

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