Heron triangles with two fixed sides

Ionascu, Eugen J.; Luca, Florian; Stanica, Pantelimon

Heron triangles with two fixed sides

Authors

Ionascu, Eugen J.

Luca, Florian

Stanica, Pantelimon

Description

In 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 2005