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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