10.46298/hrj.2019.5101
https://hrj.episciences.org/5101
Halbeisen , Lorenz
Lorenz
Halbeisen
Hungerbühler , Norbert
Norbert
Hungerbühler
A Theorem of Fermat on Congruent Number Curves
A positive integer $A$ is called a \emph{congruent number} if $A$ is the area of a right-angled 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.
episciences.org
Congruent numbers
Pythagorean triple
2010 Mathematics Subject Classification. primary 11G05; secondary 11D25
[ MATH ] Mathematics [math]
[ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]
2019-01-23
2019-01-23
2019-01-23
en
journal article
https://hal.science/hal-01983260v1
2804-7370
https://hrj.episciences.org/5101/pdf
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