UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Perfect Cuboid

 

An Euler Brick is just a cuboid, or a rectangular box, in which all of the edges (length, depth, and height) have integer dimensions; and in which the diagonals on all three sides are also integers.

 

 

 

 

 

So if the length, depth and height are a, b, and c respectively, then a, b, and c are integers, as are the quantities √(a²+b²) and √(b²+c²) and √(c²+a²).

The problem is to find a perfect cuboid, which is an Euler Brick in which the space diagonal, that is, the distance from any corner to its opposite corner, given by the formula √(a²+b²+c²), is also an integer, or prove that such a cuboid cannot exist .

 

For further information, please see:

[1] http://www.christianboyer.com/eulerbricks/

[2] http://mathworld.wolfram.com/EulerBrick.html

[3] http://f2.org/maths/peb.html

 

You can check for contributions to this problem on the solutions page.

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