U N S O L V E D :
Does there exist a rectangular box such that all of its side lengths, all of the lengths of the diagonals of the faces, and the length of the long diagonals, are all whole numbers (integers)?
Does there exist a rectangular box such that all of its side lengths, all of the lengths of the diagonals of the faces, and the length of the long diagonals, are all whole numbers (integers)?