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 was introduced for the IBM 709 and IBM 705 III computers, looked identical to the IBM 727, and used vacuum tubes. The main improvement was the use of a dual gap head permitting write verify. The IBM 729 II was introduced for the IBM 7000 series computers, introducing a new cabinet style and transistorized circuitry. Supported dual density (200, 556). High speed (112.5 in/s) single density (556). High speed (112.5 in/s) dual density (200, 556). High density (800). High speed (112.6 in/s) high density (800). Introduced September 1961. IBM 729 The IBM 729 Magnetic Tape Unit was IBM's iconic tape