== In , and in . All the following is based on Gauss' Quadratic Reciprocity Law:
== Sometimes it helps to factor out these things over the reals: in , so in every field in which 3 is a quadratic
residue we get the above factorization , and this happens in . This last kind of primes
may be expressed more simply by . Examples: , etc.
So the primes that haven't been considered are those that are but not , like , etc., and also primes which
are , like , etc., but...but then nothing: unless I made some mistake somewhere, the pol. is irreducible over since (1) 3 is not a quadratic
residue modulo 17 (and thus the pol. doesn't have a actorization in two quadratic pol's. as above), and (2) it's easy to check (this pol. is an even function...) that
no element in is a root of the pol.