made with Mathematica technology MathWorld
Algebra
Applied Mathematics
Calculus and Analysis
Discrete Mathematics
Foundations of Mathematics
Geometry
History and Terminology
Number Theory
Probability and Statistics
Recreational Mathematics
Topology
Alphabetical Index
Interactive Entries
Random Entry
New in MathWorld
MathWorld Classroom
About MathWorld
Contribute to MathWorld
Send a Message to the Team
MathWorld Book
12,903 entries
Last updated: Mon Dec 1 2008

Created, developed, and nurtured by Eric Weisstein
at Wolfram Research
Number Theory > Prime Numbers > Prime Number Properties >
Number Theory > Divisors >
History and Terminology > Disciplinary Terminology > Medical Terminology >

Carmichael Condition

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.

SEE ALSO: Carmichael Number

REFERENCES:

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. "Giuga's Conjecture on Primality." Amer. Math. Monthly 103, 40-50, 1996.




CITE THIS AS:

Weisstein, Eric W. "Carmichael Condition." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CarmichaelCondition.html

SendContact the MathWorld Team
© 1999-2008 Wolfram Research, Inc. | Terms of Use

The Wolfram Demonstrations Project Browse Topics View Latest
JUST RELEASED: Wolfram Mathematica 7
 Other Wolfram Web Resources »
Wolfram Research
Mathematica Home Page
Mathematica Documentation Center
Wolfram Demonstrations Project
Online Integrator
Functions Site
Wolfram Tones
Wolfram Science
Wolfram Blog
more…