On the greatest prime factor of sides of a Heron triangle

A Heron triangle is a triangle whose sides a, b, c and area A = s(s − a)(s − b)(s − c) are integers. Here, s = (a + b + c)/2 is the semiperimeter of . The triangle is called reduced if gcd(a, b, c) = 1. For a positive integer n let P(n) be the largest prime factor of n with the convention that P(1) = 1. In [5], it was shown that P(A) → ∞ as max{a, b, c} → ∞ through triples which are sides of reduced Heron triangles. In [4], it was shown that also P(abc) → ∞ again as max{a, b, c} → ∞ through triples which are sides of reduced Heron triangles. Here, we improve this to: Theorem 1. P(bc) goes to infinity as max{a, b, c} goes to infinity through triples which are sides of reduced Heron triangles .