The diameter of the circumcircle of a Heron triangle (Q942849)

A Heron triangle is a triangle with integer sides and integer area. In the paper under review, the author proves that a positive integer \(k\) can be the radius of the circumcenter of some Heron triangle if and only if there is one prime factor of \(k\) congruent to \(1\) modulo \(4\). This improves upon a prior result of \textit{A.-V. Kramer} and the reviewer [Acta Acad. Paedagog. Agriensis, Sect. Mat. (N.S.) 27, 25--38 (2000; Zbl 1062.11019)]. The proof is elementary and it is based on one hand on Heron's formula, and on the other hand on the fact that the only odd primes that can divide the sum of two coprime squares are the ones which are congruent to \(1\) modulo \(4\). The author also puts forward the question of characterizing which rational numbers \(k\) can be the radius of the circumcenter of some Heron triangle.