# A=x^b mod p, solvable?

Say you are given a=x^b mod p, where p, a, and b are known. Is there a way to solve this? I am pretty sure there is . . . but it is driving me nuts.

-Chu

Try solving x^2 = 2 (mod 3).

Muzza said:
Try solving x^2 = 2 (mod 3).

Sorry, I'll rephrase. I know a solution must exist from the choices of p,b,and a (this is part of a crypto algorithm where they know x, I do not, and I am wondering if I have sufficent info to solve for it).

matt grime
obviously b must divide $$\varphi(x)$$, but that doesn't give a sufficient condition for a solution, or even tell you what it is.