## 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 k0 so that for k > k0(\epsilon) k! is the product of k integers all greater than (1-\epsilon)k/e? Determine or estimate the smallest integer nk \geq 2k so that all prime factors of \binom{nk}{k} are greater than k. Selfridge and Erdös proved nk > k1+c and that nk is not monotonic.
Classif.:  * 11B65 Binomial coefficients, etc.
11B75 Combinatorial number theory
00A07 Problem books
Citations:  Zbl 214.00106(EA)

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