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Full-Text Articles in Physical Sciences and Mathematics
On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh
On The Characterization Of Prime Sets Of Polynomials By Congruence Conditions, Arvind Suresh
CMC Senior Theses
This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. 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 over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.