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**Zentralblatt MATH**

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

**Zbl.No: ** 217.03101

**Autor: ** Erdös, Paul

**Title: ** Some problems in number theory (In English)

**Source: ** Computers in Number Theory, Proc. Atlas Sympos. No.2, Oxford 1969, 405-414 (1971).

**Review: ** [For the entire collection see Zbl 214.00106.]

Several solved and unsolved problems are discussed. Here we just mention a few of them. Let m \geq 2k. Is it true that \binom{m}{k} has a divisor d satisfying cm < d < m where c is an absolute constant? Is it true that for every \epsilon > 0 there is a k_{0} so that for k > k_{0}(\epsilon) k! is the product of k integers all greater than (1-\epsilon)k/e? Determine or estimate the smallest integer n_{k} \geq 2k so that all prime factors of \binom{n_{k}}{k} are greater than k. Selfridge and Erdös proved n_{k} > k^{1+c} and that n_{k} is not monotonic.

**Classif.: ** * 11B65 Binomial coefficients, etc.

11B75 Combinatorial number theory

00A07 Problem books

**Citations: ** Zbl 214.00106(EA)

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