Let p be a prime congruent to -1 mod 4. Show that X^2 + 1 is irreducible in Z_p[X], and hence K = Z_p[X] / (X^2 + 1) is the field of order p^2. Note that K has a multiplication similar to that of the complex numbers.© BrainMass Inc. brainmass.com November 24, 2021, 4:31 pm ad1c9bdddf
Since p = -1 (mod 4), then -1 is not a quadratic residue of p. It means that the equation ...
In this solution, we provide proof that the given function is irreducible.