Heron triangles with two fixed sides

✍ Scribed by Eugen J. Ionascu; Florian Luca; Pantelimon Stănică

• Book ID: 104024846
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 181 KB
• Volume: 126
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.12.004

✦ Synopsis

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.