1995 AIME Problems/Problem 11

Problem

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

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1995 AIME Problems/Problem 11

Problem

Solution

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