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dc.contributor.author
Becher, Veronica Andrea  
dc.contributor.author
Madritsch, Manfred G.  
dc.date.available
2023-07-19T19:22:10Z  
dc.date.issued
2022-04  
dc.identifier.citation
Becher, Veronica Andrea; Madritsch, Manfred G.; On a question of Mendès France on normal numbers; Polish Academy of Sciences. Institute of Mathematics; Acta Arithmetica; 203; 3; 4-2022; 271-288  
dc.identifier.issn
0065-1036  
dc.identifier.uri
http://hdl.handle.net/11336/204518  
dc.description.abstract
In 2008 or earlier, Michel Mendès France asked for an instance of a real number x such that both x and 1/x are simply normal to a given integer base b. We give a positive answer to this question by constructing a number x such that both x and its reciprocal 1/x are continued fraction normal as well as normal to all integer bases greater than or equal to 2. Moreover, x and 1/x are computable, the first n digits of their continued fraction expansion can be obtained in O(n4) mathematical operations.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Polish Academy of Sciences. Institute of Mathematics  
dc.rights
info:eu-repo/semantics/restrictedAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
COMPUTABLE NUMBERS  
dc.subject
CONTINUED FRACTION NORMAL  
dc.subject
NORMAL NUMBERS  
dc.subject.classification
Matemática Aplicada  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
On a question of Mendès France on normal numbers  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2023-07-07T22:23:51Z  
dc.journal.volume
203  
dc.journal.number
3  
dc.journal.pagination
271-288  
dc.journal.pais
Polonia  
dc.journal.ciudad
Varsovia  
dc.description.fil
Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina  
dc.description.fil
Fil: Madritsch, Manfred G.. Centre National de la Recherche Scientifique; Francia  
dc.journal.title
Acta Arithmetica  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/online/114652/on-a-question-of-mendes-france-on-normal-numbers  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4064/aa210813-28-1  

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