Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 386.10002
Autor: Erdös, Paul; Straus, E.G.
Title: On products of consecutive integers. (In English)
Source: Number Theory and Algebra; Collect. Pap. dedic. H.B. Mann, A.E. Ross, O. Taussky-Todd, 63-70 (1977).
Review: [For the entire collection see Zbl 356.00004.]
The authors investigate various problems associated with the divisibility properties of A(n,k) = \frac{(n+k)!}{n!}. One such problem is to estimate f(n,k) which denotes the least positive integer m > n so that A(m,k) is divisible by A(n,k). Another problem relates to deciding whether for given n > 1 and all (or at least almost all) large m there exists k, where 1 \leq k \leq m-n, such that \binom{k+n}{n}|\binom{m+k}{k}.
Reviewer: S.L.G.Choi
Classif.: * 11A05 Multiplicative structure of the integers
11A07 Congruences, etc.
11B39 Special numbers, etc.
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