Halbeisen, Lorenz; Hungerbühler, Norbert A theorem of Fermat on congruent number curves. (English) Zbl 1440.11094 Hardy-Ramanujan J. 41, 15-21 (2018). Summary: 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 \(y\ne 0\). 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. Cited in 3 Documents MSC: 11G05 Elliptic curves over global fields 11D25 Cubic and quartic Diophantine equations Keywords:congruent numbers; Pythagorean triples PDFBibTeX XMLCite \textit{L. Halbeisen} and \textit{N. Hungerbühler}, Hardy-Ramanujan J. 41, 15--21 (2018; Zbl 1440.11094) Full Text: arXiv Link