## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  125.02306
Autor:  Erdös, Pál
Title:  On some divisibility properties of 2n\choose n (In English)
Source:  Can. Math. Bull. 7, 513-518 (1964).
Review:  L. Moser (Zbl 113.03606) has proved that \binom{2n}{n} = \binom{2n}{n} \binom{2b}{b} has no solution. The writer proves the following result. Denote by g(m) the smallest integer n > m such that \binom{2m}{m} | \binom{2n}{n}. Then for all m, g(m) \geq 2m, for m > m0, m1+c < g(m) < (2m) log m/ log 2 for a certain absolute constant c > 0.
Reviewer:  L.Carlitz
Classif.:  * 11B65 Binomial coefficients, etc.
Index Words:  number theory

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