On the greatest prime factor of sides of a Heron triangle (Q1006438)

A Heron triangle is a triangle with integer sides \(a,b,c\) such that its area \(A=\sqrt{s(s-a)(s-b)(s-c)}\) is also an integer, where \(s\) is the semiperimeter. It was proved by \textit{I. Gaál, I. Járási} and \textit{F. Luca} [Exp. Math. 12, No. 3, 303--310 (2003; Zbl 1096.11011)] that the greatest prime factor of \(abc\), that is \(P(abc)\) tends to infinity if \(\max (a,b,c)\) tends to infinity through triples which are sides of Heron triangles. The author proves that the same statement is valid assuming \(P(bc)\) tends to infinity. The proof applies \(S\)-unit equations.