Let S(A) be {1,2,3,...,(A-1)} and S'(A,B) be the set of elements X from S(A) that satisfy X^B mod A=1. Assuming that A is prime, find the sum of all the elements of S'(A,B) in terms of A and B.

(In reply to Is there a solution? by Eigenray)

I observed that right after you posted "Partial Solution"
There is no generalization for this sum for odd GCD values.
But one thing is that sum of all solutions in this case is 
divisible by p.

Generally, I submit solutions within a week. You can take 
it as granted that I had no solution for a problem if solution
is not posted within that time.

Posted by Praneeth on 2007-09-10 07:31:06