2006/08/07 by Eugen J. Ionascu, Eugen J. Ionaşcu, Ionascu, Eugen J. +5
Mathematics · #11A41 #11A51 #11N05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11A41 #msc:11A51 #msc:11N05
paper · pdf · doi:10.48550/arxiv.math/0608185
20 pges, no figures, submitted in 2005
arxiv created 2006/08/07 · openalex publication_date 2006/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)≤ 5 if p and q are primes, and that H(a,b)=0 for a random choice of positive integers a and b.