+319 
Perfect Cuboid Problem
Remember the pythagorean theorem, A2 + B2 = C2? The three letters correspond to the three sides of a right triangle. In a Pythagorean triangle, and all three sides are whole numbers. Let's extend this idea to three dimensions. In three dimensions, there are four numbers. In the image above, they are A, B, C, and G. The first three are the dimensions of a box, and G is the diagonal running from one of the top corners to the opposite bottom corner.
+128408
We can break this down in parts
The diagonal distance [in the same plane] across the bottom of the box will be
f =sqrt [ (d^2 -a^2) + (e^2 - a^2) ] = sqrt [ b^2 + c^2]
And f^2 = (b^2 + c^2)
Then....the height of the box = a = sqrt [ e^2 - c^2 ]
And a^2 = (e^2 - c^2)
So....by the Pythagorean Theorem....g =
sqrt [ f^2 + a^2] =
sqrt [ (b^2 + c^2) + (e^2 - c^2) ] =
sqrt [ b^2 + e^2]
