MOD calculation / reversing

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Example ->

b=104683 as a prime, c=84697 ->

root = powmod (c, (2*b + 1)/9, b) = powmod (84697, 23263, 104683) = 11484

84697 = 11484^3 MOD 104683

It is OK. But, root can be 4444 also. It is not problem for me, root can be more than one :-) I can say that the formula is working properly for prime number.

I used the library GMP and the program REXX. They gave me same result for big numbers. Unfortunately, I could not find the solution. I guess, real "b" which has 128 bytes length is not prime but composite. Now, I'll try to factorize the "b" or searching for other approach.