• Support PF! Buy your school textbooks, materials and every day products Here!

Primitive roots

  • Thread starter b0mb0nika
  • Start date
  • #1
37
0
let g be a primitive root of the odd prime p
show that -g is a primitive root or not according as
p==1 ( mod 4) or p==3(mod4)

how would i start in solving this problem
thanks
:cool:
 

Answers and Replies

  • #2
1,056
0
For p==1 Mod 4, there exists an X such that X^2 ==-1 Mod p. This is not true for p==3 Mod 4. If x is a primitive root then x^((p-1)/2) = -1 since the smallest power of x that is 1 Mod p is x^(p-1). So, those are the facts needed.
 

Related Threads for: Primitive roots

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
24
Views
4K
Replies
3
Views
2K
  • Last Post
Replies
13
Views
7K
Replies
14
Views
24K
  • Last Post
Replies
7
Views
3K
Top