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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 re: One pattern (a hint) | Comment 3 of 8 |
(In reply to One pattern by Charlie)

Try using Fermat's Little Theorem and also note that their sum is divisible by A except for the case where only 1 is the solution

Edited on July 21, 2007, 4:21 am
  Posted by Praneeth on 2007-07-21 03:14:05

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