Lorenz Halbeisen ; Norbert Hungerbühler - A Theorem of Fermat on Congruent Number Curves

hrj:5101 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5101
A Theorem of Fermat on Congruent Number CurvesArticle

Authors: Lorenz Halbeisen 1; Norbert Hungerbühler 1

  • 1 Department of Mathematics, ETH Zentrum

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 y2=x3A2x has a rational point (x,y)Q2 with y0. 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.


Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: Congruent numbers,Pythagorean triple,2010 Mathematics Subject Classification. primary 11G05; secondary 11D25,[MATH]Mathematics [math],[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

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