On the Characterization of Prime Sets of Polynomials by Congruence Conditions
نویسندگان
چکیده
This project is concerned with the set of primes modulo which some monic, irreducible polynomial f(x) ∈ Z[x] has a root, called the Prime Set of f . We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial in Z[x] is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.
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