prime factors of
We list prime factor of the binomials in , i.e. in the polynomial ring . The prime factors can always be chosen to be with integer coefficients and the number of the prime factors equals to (http://planetmath.org/TauFunction); see the proof (http://planetmath.org/FactorsOfNAndXn1).
Note 1. All factors shown above are irreducible polynomials (in the field of their own coefficients), but of course they (except ) may be split into factors of positive degree in certain extension fields; so e.g.
Note 2. The 24 examples of factorizations are true also in the fields of characteristic , but then many of the factors can be simplified or factored onwards (e.g. if the characteristic (http://planetmath.org/Characteristic) is 2).
|Title||prime factors of|
|Date of creation||2013-03-22 16:29:51|
|Last modified on||2013-03-22 16:29:51|
|Last modified by||pahio (2872)|