%0 Journal Article
%T On the Applications of Cyclotomic Fields in Introductory Number Theory
%A Kabalan Gaspard
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1110.4445v3