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How to factor a polynomial modulo p? 
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#1
Feb2412, 02:25 PM

P: 57

I can understand most of Galois Theory and Number Theory dealing with factorization and extension fields, but I always run into problems that involve factorization mod p, which I can't seem to figure out how to do. I can't find any notes anywhere either, so I was wondering if someone could give me some steps. p is prime, of course.



#2
Feb2512, 04:33 AM

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HW Helper
P: 2,020

Do you have any specific questions? For general reading material, you could try googling "factoring polynomials over finite fields".



#3
Feb2512, 09:55 AM

P: 57

www.science.unitn.it/~degraaf/compalg/polfact.pdf http://www.math.uiuc.edu/~rash/Ant/AntChapter4.pdf However, I'm still wondering what other types of finite fields it would be useful to factor over (am I correct in assuming that not all finite fields are prime fields?) 


#4
Mar512, 12:42 PM

P: 150

How to factor a polynomial modulo p?
You usually reduce the polynomial using the small Fermat theorem, x^{p} [itex]\equiv[/itex] x (mod p) for every variable x that has a power greater than p1



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