Note on squarefree integers through a set theoretical property
Abstract
In this paper, we show a property of set theory, that in number theory has the following consequence: if
are squarefree integers, then the number of distinct ratios
is greater than or equal to n, where
denotes the greatest common divisor of
and
.
![a_{1} < a_{2} < \ldots < a_{n}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/451f53619bf8bfef35cf6079711a8a1f.png)
![a_{i}/(a_{i},a_{j})](http://siba-ese.unile.it/plugins/generic/latexRender/cache/d1b927da623c597229b08eff55596ef6.png)
![(a_{i},a_{j})](http://siba-ese.unile.it/plugins/generic/latexRender/cache/944333ee523ad34327b4940b3c5b99d9.png)
![a_{i}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/d8dd7d0f3eb7145ca41c711457b7eb8f.png)
![a_{j}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/cd2d31f4876de2ca5afbffde34d0dade.png)
DOI Code:
10.1285/i15900932v19n2p227
Full Text: PDF