A Theorem of Fermat on Congruent Number Curves

Monday, 26 March, 2018

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A positive integer A is called a congruent number if A is the area of a right-angled triangle with three rational sides. Equivalently, A is a congruent number if and only if the congruent number curve y^2=x^3-A^2x has a rational point (x,y)\in\mathbb Q^2 with y\neq 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.


Lorenz Halbeisen
Norbert Hungerbühler