Year: 2014
Type: article
Abstract: Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$ be a prime and $b$ a primitive root of $p^2$ . In this paper, we give an explicit formula for the number of times a value in $\{0,1,\ldots,b-1\}$ occurs in the periodic part of the base- $b$ expansion of $1/p^m$ . As a consequence of this result, we prove two recent conjectures of Aragón Artacho et al. [‘Walking on real numbers’,Math. Intelligencer35(1) (2013), 42–60] concerning the base- $b$ expansion of Stoneham numbers.
Author: MICHAEL COONS
Institution: University of Newcastle Australia
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2023071840