How Can I Solve a Modulo Equation with Large Values?

[mathnub31]

How would one normally solve this type of equation

x^a = b (mod n)

Is there any trick to solve it if I know that n = 465992738619896000 and a = 23407534262244700, or perhaps an algorithm?

 

[Eynstone]

The existence can be checked with the help of reciprocity laws, but it's a formidable task ( to speak nothing about HOW to find x).

 

[mathwonk]

i.e, google quadratic reciprocity, for the case of a = 2.

 

[Xitami]

http://www.alpertron.com.ar/LOGDI.HTM