AN ARITHMETICAL EXCURSION VIA STONEHAM NUMBERS
Michael James Coons · 2014
Let p be a prime and b a primitive root of p². In this paper, we give an explicit formula for the number of times a value in {0, 1, ..., b - 1} occurs in the periodic part of the base-b expansion of 1/pm. As a consequence of this result, we prove two recent conjectures of Aragón Artacho et al. [‘Walking on real numbers’, Math. Intelligencer 35(1) (2013), 42–60] concerning the base-b expansion of Stoneham numbers.