Tesis
A função [Phi] de Euler e a expansão periódica de frações na base b
Fecha
2015-03-27Registro en:
RECH, Marcionei. A função [Phi] de Euler e a expansão periódica de frações na base b. 2015. 57 f. Dissertação (Mestrado Profissional em Matemática - PROFMAT) - Universidade Federal de Mato Grosso, Instituto de Ciências Exatas e da Terra, Cuiabá, 2015.
Autor
Araújo, Martinho da Costa
http://lattes.cnpq.br/3950386824945565
Araújo, Martinho da Costa
054.543.674-72
http://lattes.cnpq.br/3950386824945565
Leite, Daniel Carlos
877.530.731-68
http://lattes.cnpq.br/2518754887213098
054.543.674-72
Ramos, José Ivan da Silva
164.756.312-72
http://lattes.cnpq.br/0315850569914268
Institución
Resumen
This study aims to explore the behavior of the expansion of common fractions, the length
of the non-periodic part and the period if it is an infinite tithe, with the aid of ϕ Euler
function. Besides the decimal expansions, which are the most common, we will explore the
expansions using any base b, or another numbering system, in order to generalize some
results that are easily observed in the decimal number system. We shall resume some
concepts: number systems, prime numbers, the function ϕ of Euler and Euler’s Theorem,
which are important to base our discussions. We will show some examples of expansion
of common fractions for different numerical bases resulting in finite decimals, and simple
and composite periodic decimals.