MathDB
Right Prism

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December 22, 2005
geometry3D geometryprismcalculusintegrationratiorectangle

Problem Statement

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