Heron triangles with two fixed sides

Eugen J. Ionascu; Florian Luca; Pantelimon Stanica

Heron triangles with two fixed sides

数论 2007-05-23 v1

作者: Eugen J. Ionascu , Florian Luca , Pantelimon Stanica

摘要

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 $b$ .

引用

@article{arxiv.math/0608185,
  title  = {Heron triangles with two fixed sides},
  author = {Eugen J. Ionascu and Florian Luca and Pantelimon Stanica},
  journal= {arXiv preprint arXiv:math/0608185},
  year   = {2007}
}

备注

20 pges, no figures, submitted in 2005

Heron triangles with two fixed sides

摘要

引用

备注

相关论文