๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Fermat Quotients for Composite Moduli

โœ Scribed by Takashi Agoh; Karl Dilcher; Ladislav Skula


Book ID
102601610
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
363 KB
Volume
66
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis


Analogues of Fermat quotients for a composite modulus m 2 are investigated, with special emphasis on various congruences. In particular, the numbers m for which a ,(m) #1 (mod m 2 ), where gcd(a, m)=1, (``Wieferich numbers with base a'') are completely characterized in terms of the Wieferich primes with base a.


๐Ÿ“œ SIMILAR VOLUMES


Pseudorandomness and Dynamics of Fermat
โœ Ostafe, Alina; Shparlinski, Igor E. ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› Society for Industrial and Applied Mathematics ๐ŸŒ English โš– 273 KB
Artin's Conjecture on Average for Compos
โœ Shuguang Li ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 201 KB

Let a be an integer { &1 and not a square. Let P a (x) be the number of primes up to x for which a is a primitive root. Goldfeld and Stephens proved that the average value of P a (x) is about a constant multiple of xร‚ln x. Carmichael extended the definition of primitive roots to that of primitive \*