Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 146.05304
Autor: Erdös, Pál
Title: On the multiplicative representation of integers (In English)
Source: Isr. J. Math. 2, 251-261 (1964).
Review: Let b1 < b2 < ··· be an infinite sequence of integers and g(n) the number of solutions of n = bibj. It is shown that if g(n) > 0 for all n > n0 then limsupn ––> oo g(n) = oo. A proof of the following result is outlined. Denote by ul(n) the smallest integer so that if b1 < ··· < bt \leq n, t \leq ul(n) is any sequence of integers then forsome m, g(m) \geq l. If 2k-1 < l \leq 2k then ul(n) = (1+o(1))n(log log n)k-1/(k-1)! log n. {There are numerous minor misprints including the denominator in (6) which should be read as Nr ½^{r-1}.}
Reviewer: R.C.Entringer
Classif.: * 11A67 Representation systems for integers and rationals
11B75 Combinatorial number theory
Index Words: number theory
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