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3.3.5 Polynomials Modulo Primes
Mathematica can work with polynomials whose coefficients are in the finite field  of integers modulo a prime 
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Functions for manipulating polynomials over finite fields.
Here is an ordinary polynomial.
In[1]:= Expand[ (1 + x)^6 ]
Out[1]= 
This reduces the coefficients modulo 2.
In[2]:= PolynomialMod[%, 2]
Out[2]= 
Here are the factors of the resulting polynomial over the integers.
In[3]:= Factor[%]
Out[3]= 
If you work modulo 2, further factoring becomes possible.
In[4]:= Factor[%, Modulus->2]
Out[4]= 
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