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Topics In Cyclotomic And Quadratic Fields, Pam Mellinger

Honors Theses

This paper introduces cyclotomic and quadratic fields and explores some of their properties and applications to problems in number theory. After some preliminary definitions and theorems, the paper looks at the relationship between quadratic and cyclotomic fields, at Kummer's lemma on units in the pth cyclotomic field, and at the Quadratic Reciprocity Law and its applications to diophantine equations.