Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the $p$-divisibility of Fermat quotients


Authors: R. Ernvall and T. Metsänkylä
Journal: Math. Comp. 66 (1997), 1353-1365
MSC (1991): Primary 11A15, 11Y70; Secondary 11D41, 11R18
MathSciNet review: 1408373
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The authors carried out a numerical search for Fermat quotients $Q_{a} = (a^{p-1}-1)/p$ vanishing mod $p$, for $1 \le a \le p-1$, up to $p < 10^{6}$. This article reports on the results and surveys the associated theoretical properties of $Q_{a}$. The approach of fixing the prime $p$ rather than the base $a$ leads to some aspects of the theory apparently not published before.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11A15, 11Y70, 11D41, 11R18

Retrieve articles in all journals with MSC (1991): 11A15, 11Y70, 11D41, 11R18


Additional Information

R. Ernvall
Affiliation: Forssa Institute of Technology, Saksankatu 46, FIN-30100 Forssa, Finland

T. Metsänkylä
Affiliation: Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
Email: taumets@sara.cc.utu.fi

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00843-0
PII: S 0025-5718(97)00843-0
Keywords: Fermat quotients, computation, Fermat's equation, Catalan's equation, cyclotomic fields
Received by editor(s): March 4, 1996
Received by editor(s) in revised form: May 22, 1996
Article copyright: © Copyright 1997 American Mathematical Society