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Sum of all solutions (Posted on 2007-07-20) Difficulty: 2 of 5
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.

No Solution Yet Submitted by Praneeth    
Rating: 4.5000 (4 votes)

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Hints/Tips Hint2 | Comment 4 of 8 |
Its a cyclic sequence of (A-1) entries.
Now take GCD of A-1 and Bmod(A-1).
All the possible B values from 1 to A-1 with the same GCD,
have the same sum. Now take cases of odd and even values of B.
 

  Posted by Praneeth on 2007-07-25 08:47:48
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