A right rectangular prism \(P_{}\) (i.e., a rectangular parallelpiped) has sides of integral length \(a, b, c,\) with \(a\le b\le c.\) A plane parallel to one of the faces of \(P_{}\) cuts \(P_{}\) into two prisms, one of which is similar to \(P_{},\) and both of which have nonzero volume. Given that \(b=1995,\) for how many ordered triples \((a, b, c)\) does such a plane exist?

(第十三届AIME1995 第11题)