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arXiv · 1110.4445

On the Applications of Cyclotomic Fields in Introductory Number Theory

Kabalan Gaspard
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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.

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Kabalan Gaspard. 2011-10-20. On the Applications of Cyclotomic Fields in Introductory Number Theory. https://arxiv.org/abs/1110.4445

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