ERDŐS’ METHOD FOR DETERMINING THE IRRATIONALITY OF PRODUCTS

This paper deals with a sufficient condition for the infinite product of rational numbers to be an irrational number. The condition requires only some conditions for convergence and does not use other properties like divisibility. The proof is based on an idea of Erdős.

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Bibliographic Details
Published inBulletin of the Australian Mathematical Society Vol. 84; no. 3; pp. 414 - 424
Main Authors HANČL, JAROSLAV, KOLOUCH, ONDŘEJ
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2011
Subjects
primary 11J72
irrationality
infinite products
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Summary:This paper deals with a sufficient condition for the infinite product of rational numbers to be an irrational number. The condition requires only some conditions for convergence and does not use other properties like divisibility. The proof is based on an idea of Erdős.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972711002309