episciences.org_5101_1653282397
1653282397
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
23
2019
A Theorem of Fermat on Congruent Number Curves
Lorenz
Halbeisen
Norbert
Hungerbühler
A positive integer $A$ is called a \emph{congruent number} if $A$ is the area of a rightangled triangle with three rational sides. Equivalently, $A$ is a \emph{congruent number} if and only if the congruent number curve $y^2 = x^3 − A^2 x$ has a rational point $(x, y) \in {\mathbb{Q}}^2$ with $y \ne 0$. Using a theorem of Fermat, we give an elementary proof for the fact that congruent number curves do not contain rational points of finite order.
01
23
2019
5101
https://hal.archivesouvertes.fr/hal01983260v1
10.46298/hrj.2019.5101
https://hrj.episciences.org/5101

https://hrj.episciences.org/5101/pdf