Proving special cases of Fermat's last theorem by using the classical approach of inspecting the ring $\mathbb{Z} [e^\frac{2\pi i}{p}]$ for primes $p$

Jonge, Dylan de (2025) Proving special cases of Fermat's last theorem by using the classical approach of inspecting the ring $\mathbb{Z} [e^\frac{2\pi i}{p}]$ for primes $p$. Bachelor's Thesis, Mathematics.

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Abstract

In this project we investigate the ring $\mathbb{Z}[\zeta_n]$ for certain small values of $n$. We determine the unit groups and show these rings take on unique factorization. These results allow us to prove Fermat's last theorem for these specific values of $n$. We also briefly discuss some key results for $\mathbb{Z}[\zeta_n]$ where $n$ is any prime number and use those for the first case of Fermat's last theorem for suitable $n$.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Top, J. and Ozman, E.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	04 Jul 2025 13:05
Last Modified:	15 Jul 2025 10:29
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/35634

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