Heron triangles with two fixed sides

Abstract: In this paper, we study the function , 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 if p and q are primes, and that for a random choice of positive integers a and b. [Copyright &y& Elsevier]