𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the distribution of the order and index of over residue classes—I

✍ Scribed by Pieter Moree

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
380 KB
Volume
114
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

For a fixed rational number g / ∈ {-1, 0, 1} and integers a and d we consider the set N g (a, d) of primes p for which the order of g (mod p) is congruent to a (mod d). For d = 4 and 3 we show that, under the generalized Riemann hypothesis (GRH), these sets have a natural density g (a, d) and compute it. The results for d = 4 generalise earlier work by Chinen and Murata. The case d = 3 was apparently not considered before.

📜 SIMILAR VOLUMES

On Arithmetic Properties of Integers wit
On Arithmetic Properties of Integers with Missing Digits I: Distribution in Residue Classes
✍ Paul Erdős; Christian Mauduit; András Sárközy 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 337 KB

Consider all the integers not exceeding x with the property that in the system number to base g all their digits belong to a given set D/[0, 1, ..., g, &1]. The distribution of these integers in residue classes to ``not very large'' moduli is studied. 1998 Academic Press SECTION 1 Throughout this pa