On the Applications of Cyclotomic Fields in Introductory Number Theory
Number Theory
2012-05-30 v3
Abstract
In this essay, we see how prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime) can lead to elegant proofs of number theoretical concepts. We namely develop the notion of primary units in a cyclotomic field, demonstrate their equivalence to real units in this case, and show how this leads to a proof of a special case of Fermat's Last Theorem. We finally modernize Dirichlet's solution to Pell's Equation.
Keywords
Cite
@article{arxiv.1110.4445,
title = {On the Applications of Cyclotomic Fields in Introductory Number Theory},
author = {Kabalan Gaspard},
journal= {arXiv preprint arXiv:1110.4445},
year = {2012}
}