# Modulo arthmetic solve for x^N .

1. Nov 16, 2009

Modulo arthmetic solve for x^N.....

Hay all, I am stuck on a problem, and its driving me crazy. I have a problem, xN = a mod b. Where I have to solve for x. My first thought was use to Fermat's little theorem(if I have the name correct), however my b is not a prime, (neither is 'N' or 'a' for that fact). I can give the exact problem with numbers if needed, but thought it would be slightly easier with variables instead. Any tips on how I could start to solve this would be great. Any questions please ask.

2. Nov 16, 2009

### ramsey2879

Re: Modulo arthmetic solve for x^N.....

I believe there is no generic solution to this problem.

3. Nov 16, 2009

### Matthollyw00d

Re: Modulo arthmetic solve for x^N.....

Giving the actual numbers would probably be best for this one.

4. Nov 16, 2009

### Petek

Re: Modulo arthmetic solve for x^N.....

Google nth power residue for lots of results (and references to specific number theory texts) regarding your question.

Petek

5. Nov 16, 2009

### Hurkyl

Staff Emeritus
Re: Modulo arthmetic solve for x^N.....

Chinese remainder theorem.

6. Nov 17, 2009

### CRGreathouse

Re: Modulo arthmetic solve for x^N.....

Yes. Factor b, use Fermat, then CRT the results together.