Abstract
In this chapter we describe a technique for deciding whether a given polynomial in ℤp[x], p an odd prime, has an odd or an even number of distinct irreducible factors. The theorem is this:Stickelberger“s Theorem. Let p be an odd prime, f a monk polynomial of degree d with coefficients in ℤp[x], without repeated roots in any splitting field. Let r be the number of irreducible factors of f in ℤp[x]. Then r≡d (mod 2) iff the discriminant D(f) is a square in ℤp. .
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