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)