Powers of two modulo powers of three

Coons, Michael ; Winning, Heath

Journal of integer sequences, Tome 18 (2015) no. 6

Résumé

Since 2 is a primitive root of $3^{m}$ for each positive integer $m$, the set of points ${ (n, 2^{n}$ mod $3^{m}) : n \ge 0}$, viewed as a subset of $Z_{\ge 0} \times Z_{\ge 0}$ is bi-periodic, with minimal periods φ$(3^{m})$ (horizontally) and $3^{m}$ (vertically). We show that if one considers the classes of $n$ modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of Stoneham numbers.

Détail

Keywords: primitive root, strong normality, normality