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Heron triangles with two fixed sides

Eugen J. Ionascu·Florian Luca·Pantelimon Stanica
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Abstract

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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Eugen J. Ionascu, Florian Luca, Pantelimon Stanica. 2006-08-07. Heron triangles with two fixed sides. https://arxiv.org/abs/math/0608185

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