*a*,

*b*,

*c*, and

*d*so that

*a*

^{2}+

*b*

^{2}+

*c*

^{2}=

*d*

^{2}, or if that was an open problem. He added that he'd heard that Egyptians stretched ropes to create 3-4-5 triangles in order to form right angles, and was wondering about the possibility of a three-dimensional analog.

I mentioned the Google Group investigating the harder problem of finding a rectangular box with integer sides, integer diagonals, and integer main diagonal. (See http://groups.google.com/group/theperfectcuboid?lnk=iggc.)

But only while driving home did it occur to me that it's straightforward to produce lots of examples of my colleague's easier problem.

Start with your favorite primitive Pythagorean triple (

*a*,

*b*,

*c*). (See my earlier post about Pythagorean triples: http://byoshiwara.blogspot.com/2009/12/blog-post.html.)

Then

*c*is odd, so

*c*= 2

*n*+ 1, and

*a*

^{2}+

*b*

^{2}+ [2

*n*(

*n*+ 1)]

^{2}= [2

*n*(

*n*+ 1) + 1]

^{2}

For example, 3

^{2}+ 4

^{2}+ 12

^{2}= 13

^{2}.