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11.8.8  Division in ℤ/pℤ or in ℤ/pℤ[x]

The / operator divides two integers in ℤ/pℤ or two polynomials A and B in ℤ/pℤ[x]. (See also Section 7.3.2.) Since ℤ/pℤ is only a field if p is prime, the quotient is only guaranteed to exist if p is prime (unless the denominator is 0 (mod p )).

For integers in ℤ/pℤ.

Since 13 is prime:

5%13/2%13
     

−4
%13
          

Since 3(mod 14 ) is invertible in Z/14ℤ:

5%14/3%14
     

−3
%14
          

Since 7(mod 14 ) is not invertible in Z/14ℤ, this results in an error:

5%14/7%14
     
Not invertible Error: Bad Argument Value           
For polynomials.

The result of P/Q is its irreducible representation in ℤ/pℤ[x]:

(2*x^2+5)%13/(5*x^2+2*x-3)%13
     

6%13
x+1%13

2%13
x+
2%13
%13
          

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