Wilson’s theorem for prime powers
For prime and
Proof: We pair up all factors of the product into those numbers where and those where this is not the case. So is congruent (modulo ) to the product of those numbers where .
Let be an odd prime and . Since , implies either or . This leads to
for odd prime and any .
Now let and . Then
For , but for
|Title||Wilson’s theorem for prime powers|
|Date of creation||2013-03-22 13:22:14|
|Last modified on||2013-03-22 13:22:14|
|Owner||Thomas Heye (1234)|
|Last modified by||Thomas Heye (1234)|
|Author||Thomas Heye (1234)|