Fermat’s little theorem
Theorem (Fermat’s little theorem).
If with a prime and , then
If we take away the condition that , then we have the congruence relation
While it is true that prime implies the congruence relation above, the converse is false (as hypothesized by ancient Chinese mathematicians). A well-known example of this is provided by setting and . It is easy to verify that . A positive integer satisfying is known as a pseudoprime of base . Fermat little theorem says that every prime is a pseudoprime of any base not divisible by the prime.
|Title||Fermat’s little theorem|
|Date of creation||2013-03-22 11:45:08|
|Last modified on||2013-03-22 11:45:08|
|Last modified by||CWoo (3771)|