<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some lemmas for convenient work with numbers (including the proof that the sequence of prime reciprocals diverges [1]) according to [18] which were absent in the Mizar Mathematical Library. Some of them were expressed in terms of clusters’ registrations, enabling automatization machinery available in the Mizar system. Our main result of the article is in the final section; we proved that the lattice of positive divisors of a positive integer n is Boolean if and only if n is square-free.</p></abstract>

In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some lemmas for convenient work with numbers (including the proof that the sequence of prime reciprocals diverges [1]) according to [18] which were absent in the Mizar Mathematical Library. Some of them were expressed in terms of clusters’ registrations, enabling automatization machinery available in the Mizar system. Our main result of the article is in the final section; we proved that the lattice of positive divisors of a positive integer n is Boolean if and only if n is square-free.

On Square-Free Numbers

Institute of Informatics University of Białystok Akademicka 2, 15-267 Białystok Poland

Formalized Mathematics

{"article-title":"On Square-Free Numbers"}

In the article the formal characterization of square-free numbers is shown; in this manner the paper is the continuation of [19]. Essentially, we prepared some...

On Square-Free Numbers

Published Online: Jun 01, 2013

Page range: 153 - 162

DOI: https://doi.org/10.2478/forma-2013-0017

Keywords
square-free numbers, prime reciprocals, lattice of natural divisors

This content is open access.

On Square-Free Numbers

Published Online: Jun 01, 2013

Page range: 153 - 162

DOI: https://doi.org/10.2478/forma-2013-0017

Keywordssquare-free numbers, prime reciprocals, lattice of natural divisors

This content is open access.

Keywords
square-free numbers, prime reciprocals, lattice of natural divisors