Heron Triangles with Two Fixed Sides

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., it has integral area. In particular, we prove that H(p, q) 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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Document Details

Document Type
Technical Report
Publication Date
Oct 08, 2006
Accession Number
ADA573089

Entities

People

  • Eugen J. Ionascu
  • Florian Luca
  • Pantelimon Stanica

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Equations
  • Geometry
  • Information Operations
  • Integrals
  • Mathematics
  • Number Theory
  • Numbers
  • Polynomials
  • Prime Numbers
  • Rational Numbers
  • Real Numbers
  • Theorems
  • Triangles
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.