Cube (algebra) however, easy to show that most numbers are not perfect cubes because "all" perfect cubes must have digital root 1, 8 or 9. That is their values modulo 9 may be only −1, 1 and 0. Moreover, the digital root of any number's cube can be determined by the remainder the number gives when divided by 3: Every positive integer can be written as the sum of nine (or fewer) positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine positive cubes: The equation has
IBM 729 IBM 729 The IBM 729 Magnetic Tape Unit was IBM's iconic tape mass storage system from the late 1950s through the mid-1960s. Part of the IBM 7 track family of tape units, it was used on late 700, most 7000 and many 1400 series computers. Like its predecessor, the IBM 727 and many successors, the 729 used 1/2 inch (12.7 mm) magnetic tape up to 2400 feet (730 m) long wound on reels up to 10½ inch (267 mm) diameter. To allow rapid tape acceleration (and thus reduced seek/access times), long vacuum columns were placed between the tape reels and