Prime congruence problem

  • #1

Main Question or Discussion Point

Question: Suppose p and q are distinct primes. Show that p^(q-1) + q^(p-1) is congruent to 1 modulo pq.

Answer: I know from Little Fermat Theorem that p^(q-1) is congruent to 1 modulo q and q^(p-1) is congruent to 1 modulo p, but I have no idea how to combine these two.
 

Answers and Replies

  • #2
CRGreathouse
Science Advisor
Homework Helper
2,820
0
You know from the CRT that there is only one residue class mod pq that gives you A mod p and B mod q. So if 1 mod pq gives 1 mod p and 1 mod q, then you're done.
 

Related Threads for: Prime congruence problem

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
9
Views
3K
Replies
9
Views
6K
  • Last Post
Replies
19
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
10
Views
3K
Top