Structure of associated sets to Midy’s property.

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dc.contributor.authorCastillo, John H.
dc.contributor.authorGarcía Pulgarín, Gilberto
dc.contributor.authorVelásquez Soto, Juan Miguel
dc.date.accessioned2013-08-09T15:45:14Z
dc.date.available2013-08-09T15:45:14Z
dc.date.issued2013-08-09
dc.description.abstractLet b be a positive integer greater than 1, N a positive integer relatively prime to b, |b|N the order of b in the multiplicative group UN of positive integers less than N and relatively primes x to N, and x ∈ UN . It is well known that when we write the fraction N in base b, it is periodic. x Let d, k be positive integers with d ≥ 2 and such that |b|N = dk and N = 0.a1 a2 · · · a|b|N with the bar indicating the period and ai are digits in base b. We separate the period a1 a2 · · · a|b|N in d blocks of length k and let Aj = [a(j−1)k+1 a(j−1)k+2 · · · ajk ]b be the number represented in d base b by the j − th block and Sd (x) = j=1 Aj . If for all x ∈ UN , the sum Sd (x) is a multiple of bk − 1 we say that N has Midy’s property for b and d. In this work we present some interesting properties of the set of positive integers d such that N has Midy’s property to for b and d.spa
dc.identifier.urihttps://hdl.handle.net/10893/4908
dc.language.isoengspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.subjectPeriodspa
dc.subjectDecimal Representationspa
dc.subjectMultiplicative group of units modulo Nspa
dc.subjectOrder of an integerspa
dc.titleStructure of associated sets to Midy’s property.spa
dc.typeArtículo de revistaspa
dspace.entity.typePublication
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