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Heron triangles with two fixed sides

Authors
  • Ionascu, Eugen J.
  • Luca, Florian
  • Stanica, Pantelimon
Type
Preprint
Publication Date
Aug 07, 2006
Submission Date
Aug 07, 2006
Identifiers
arXiv ID: math/0608185
Source
arXiv
License
Unknown
External links

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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