Heron triangles with two fixed sides

Details Heron triangles with two fixed sides Heron triangles with two fixed sides

2006-08-07

arxiv.org/abs/math/0608185v1

Mathematics

Number Theory

20 pges, no figures, submitted in 2005

Scientific paper

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 $b$.

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