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**Zentralblatt MATH**

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

**Zbl.No: ** 014.01104

**Autor: ** Erdös, Pál

**Title: ** A generalization of a theorem of Besicovitch. (In English)

**Source: ** J. London Math. Soc. 11, 92-98 (1936).

**Review: ** Let \delta_{a} denote the density of the set consisting of all numbers which have a divisor between a and 2a. It was proved by *A.S.Besicovitch* (see Zbl 009.39504) that **liminf**_{a ––> oo} \delta_{a} = 0. Let d_{a} denote the density of the set consisting of all numbers which have a divisor between a and a^{1+\epsilona}. The author proves that if \epsilon ––> 0 as a ––> oo then d_{a} ––> 0. This is easily seen to be the best possible result of its kind. It is impossible to given a sketch of the highly ingenious proof within the limits of a review.

**Reviewer: ** Davenport (Cambridge)

**Classif.: ** * 11N25 Distribution of integers with specified multiplicative constraints

**Index Words: ** Number theory

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