A Derivation of the Infinitude of Primes

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dc.contributor.authorPasten, Hector
dc.date.accessioned2025-01-20T17:11:40Z
dc.date.available2025-01-20T17:11:40Z
dc.date.issued2024
dc.description.abstractThe well-known analogy between polynomials and integers breaks down when it comes to considering the polynomial derivative. This is rather unfortunate since derivatives are a powerful tool for doing arithmetic with polynomials. Nevertheless, there are some proposals in the literature for arithmetic analogues of derivatives. In this article we use one of these arithmetic derivatives to give a proof of the infinitude of primes which is analogous to an argument that will be presented for polynomials using polynomial derivatives. We hope that this "differential" proof of the infinitude of primes will help to motivate the reader to look for good notions of arithmetic derivatives.
dc.description.funderThis article was possible thanks to the support of ANID Fondecyt Regular Grants 1190442 and 1230507 from Chile. I thank Ricardo Menares and Natalia Garcia-Fritz for valuable feedback on a first version of this article. I also thank the referees and editors
dc.fuente.origenWOS
dc.identifier.doi10.1080/00029890.2023.2261821
dc.identifier.eissn1930-0972
dc.identifier.issn0002-9890
dc.identifier.urihttps://doi.org/10.1080/00029890.2023.2261821
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91199
dc.identifier.wosidWOS:001079297800001
dc.issue.numero1
dc.language.isoen
dc.pagina.final73
dc.pagina.inicio66
dc.revistaAmerican mathematical monthly
dc.rightsacceso restringido
dc.subject11A41
dc.subject11C08
dc.titleA Derivation of the Infinitude of Primes
dc.typeartículo
dc.volumen131
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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