Giuseppina Anatriello†, Enrico D’Amora‡ , Dino Festi§ , Giovanni Vincenzi¶
Abstract: A Pythagorean triangle is a right triangle where the lengths of the three sides are all integers. The most famous example of a Pythagorean triangle is the 3 − 4 − 5 triangle, where the lengths of the sides are 3, 4, and 5 units, respectively. In this short note, we will study the class of Pythagorean triangles that may be associated with a square by means of a real parameter k. It turns out that the triangle 3 − 4 − 5 holds exclusive property in terms of the rationality of k.
Keywords: Pythagorean triangles, elliptic curves.
MSC: 11E25 , 14H52, 97I40.
DOI 10.56082/annalsarscimath.2025.3.163
† anatriello@unina.it, Dipartimento di Architettura, Universita di Napoli ”Federico II”, Napoli, Italy
‡ edamora@unisa.it, Dipartimento di Matematica, Universita di Salerno, via Giovanni Paolo II, Fisciano, Salerno, Italy
§ dino.festi@unina.it, Dipartimento di Matematica, Universita di Napoli ”Federico II”, Napoli, Italy
¶ vincenzi@unisa.it, Dipartimento di Matematica, Universita di Salerno, via Giovanni Paolo II, Fisciano, Salerno, Italy
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 3, 2025
