2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115322In this paper, we study the function $H(a,b)$, which associates to every pair of positive integers $a$ and $b$ the number of positive integers $c$ such that the triangle of sides $a,b$ and $c$ is Heron, i.e., has integral area. In particular, we prove that $H(p,q)\le 5$ if $p$ and $q$ are primes, and that $H(a,b)=0$ for a random choice of positive integers $a$ and $b$.20 pges, no figures, submitted in 2005Number Theory11A41,11A51,11N05text