Year: 2025
Type: article
Abstract: We give a negative answer to the question by Paul Erdős and Ronald Graham on whether the series ∑n=1∞1(n+1)(n+2)⋯(n+f(n)) has irrational sum whenever (f(n))∞n=1 is a sequence of positive integers converging to infinity. To achieve this, we generalize a classical observation of Sōichi Kakeya on the set of all subsums of a convergent positive series. We also discuss why the same problem is likely difficult when (f(n))∞n=1 is additionally assumed to be increasing.
Source: Colloquium Mathematicum
Authors: Tonći Crmarić, Vjekoslav Kovač
Institutions: University of Split, University of Zagreb
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Hrvatska Zaklada za Znanost
OpenAlex ID: W4414411560
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