Fermat's assertion about primes of the form x² + 3y²

Author

• Olimpia. Lukacs

Date of Award

2007

Document Type

Dissertation/Thesis

Submission Date

October 2026

Abstract

Fermat's assertion that "every prime number which surpasses by one a multiple of three [sic] is composed of a square and the triple of another square" raises further questions about primes and other quadratic forms. The interest over primes does not stop at x² + 3y², although this form by itself is a complex way of analyzing simple primes. We present an algorithm for solving p= x² + 3y², first discovered by Lagrange, and show that this algorithm does not work for other representations of numbers by quadratic forms.

Comments

by Olimpia Lukacs.

Recommended Citation

Lukacs, Olimpia., "Fermat's assertion about primes of the form x² + 3y²" (2007). Harriet L Wilkes Honors College Theses 2003 - 2009. 44.
https://digitalcommons.fau.edu/etd_honors_1/44

Extent

v, 23 leaves : ill.

Identifier

314712617