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| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Jastrzębska, Magdalena | - |
| dc.contributor.author | Grabowski, Adam | - |
| dc.date.accessioned | 2026-10-29T08:31:00Z | - |
| dc.date.available | 2026-10-29T08:31:00Z | - |
| dc.date.issued | 2006 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 14, Issue 1, Pages 29-36 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/21358 | - |
| dc.description | This is a part of the author's MSc thesis. | pl |
| dc.description.abstract | We formalized some basic properties of the Möbius function which is defined classically as μ(n) = 1, if n = 1; μ(n) = 0, if p² | n for some prime p; μ(n) = (−1)ʳ, if n = p₁p₂⋯pᵣ, where pᵢ are distinct primes, as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function. The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors. The formalization (which is very much like the one developed in Isabelle proof assistant connected with Avigad’s formal proof of Prime Number Theorem) was done according to the book [13]. | pl |
| dc.description.sponsorship | This work has been partially supported by the KBN grant 4 T11C 039 24 and the FP6 IST grant TYPES No. 510996. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | - |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | - |
| dc.title | On the Properties of the Möbius Function | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2008 Magdalena Jastrzebska, Adam Grabowski, published by University of Białystok | pl |
| dc.rights.holder | This work is licensed under the Creative Commons License. | pl |
| dc.identifier.doi | 10.2478/v10037-006-0005-0 | - |
| dc.description.Affiliation | Magdalena Jastrzębska - Institute of Mathematics, University of Białystok | pl |
| dc.description.Affiliation | Adam Grabowski - Institute of Mathematics, University of Białystok | pl |
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| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 14 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 29 | pl |
| dc.description.lastpage | 36 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2006, Volume 14, Issue 1 | |
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