Square root of 1 with mod how to prove it?

  • #1
I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k.
However, I don't know how to give a formal proof to it.
I simply want to bypass the generalized form x^2 = a (mod n).
How can I prove it directly?
Thank you.
 

Answers and Replies

  • #2
CRGreathouse
Science Advisor
Homework Helper
2,820
0
Hmm... assuming it holds mod p^k, you could just CRT the results together.
 

Related Threads on Square root of 1 with mod how to prove it?

Replies
2
Views
877
  • Last Post
Replies
8
Views
36K
Replies
25
Views
6K
  • Last Post
Replies
1
Views
1K
  • Last Post
2
Replies
27
Views
7K
Replies
2
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
4
Views
12K
  • Last Post
Replies
4
Views
6K
Top