Abstract
Fermat’s last theorem is used to motivate the introduction of certain number fields.
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Notes
- 1.
Fermat’s last theorem was finally proved in 1993-94 by Andrew Wiles using concepts from the theory of elliptic curves.
- 2.
\(\mathbb {Q}[\omega ]=\{a_0 + a_1\omega +\cdots +a_{p-2}\omega ^{p-2}:a_i \in \mathbb {Q}\, \forall i\}\);
\(\mathbb {Z}[\omega ]=\{a_0 + a_1\omega +\cdots +a_{p-2}\omega ^{p-2}:a_i \in \mathbb {Z}\, \forall i\}\).
- 3.
In fact, this discovery is due to Kummer. See Harold Edwards’ book review in the Bulletin of the American Mathematical Society, 2 (1980), p. 327.—Ed.
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Marcus, D.A. (2018). A Special Case of Fermat’s Conjecture. In: Number Fields. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-90233-3_1
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