A função ϕ de Euler e a expansão periodica de frações na base b

Martinho Da Costa Araujo

A função ϕ de Euler e a expansão periodica de frações na base b

Martinho Da Costa Araujo

Resumo

Queremos aqui explorar o comportamento da expansão de frações ordinárias, o comprimento da parte não periódica, bem como do período se ela for uma dízima infinita, com o auxilio da função ϕ de Euler. Além das expansões decimais que são as mais comuns, exploraremos as expansões para uma base b qualquer. Apresentaremos alguns exemplos de expansões de frações ordinárias para diferentes bases numéricas gerando dízimas finitas, como também, dízimas periódicas simples e compostas.

Palavras-chave

Dízimas periódicas; bases numéricas; números racionais

Texto completo:

PDF

Revista Ciências Exatas e Naturais - RECEN. Universidade Estadual do Centro-Oeste - UNICENTRO/PR, BRASIL.

Licenciada sob uma Licença Creative Common

ISSN 2175-5620 ON LINE; 1518-0352 IMPRESSO

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`0` Logs	`0` Errors
`1` Memory	`1` Speed

memory	265,12 kB string: PKPApplication::construct
speed	0.061 ms PKPApplication::construct

A função ϕ de Euler e a expansão periodica de frações na base b

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