Digital root sequence of a rational number

• Autor(a) principal: Costa, Eudes Antonio
• Data de Publicação: 2022
• Outros Autores: Souza, Keidna Cristiane Oliveira
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/5326
• topic: Congruence; Digital Root; Rational Number; Congruência; Soma Iterada de Algarismos; Número Racional

In this, we study the digital sum application, S, for rational numbers. The applications S is well known in integers, mainly in olympic problems (IZMIRLI, 2014; ZEITZ, 1999). Costa et al. (2021) extended the application S and to a positive rational number x with finite decimal representation. We highlight the following results: given a positive rational number x, with finite decimal representation, and the sum of its digits 9, then when x is divided by powers of 2 or 5, the resulting number the digital root is equal to 9. These properties were motivated by the statement attributed to Nikola Tesla (1856-1943) (COSTA et al., 2021), that by dividing (or multiplying) consecutively by 2 the numbers of the angle 360º, geometrically associated with a circumference, the resulting angles (measured in degree) have the property that the sum of the figures is (always) equal to 9. For example, we have that S(360) = 9, so we will also have that S(180) = S(90) = S(45) = S(22.5) = S(11.25) = 9. In these notes we will extend the application S to a positive rational number x. Our intent is to present some properties and applications for every number x E Q+.