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
Pennsylvania Route 729 during the 1930s and early 1940s. Pennsylvania Route 729 Pennsylvania Route 729 (PA 729) is a , north–south state highway located in Clearfield County, Pennsylvania. The southern terminus is at PA 253/PA 453 in Gulich Township. The northern terminus is at US 219/PA 879 in Grampain. PA 729 is known by two names along its route. The two names it goes by are Main Street, and more commonly, the Tyrone Turnpike. The route begins at the village of Janesville at an intersection of PA 253/PA 453. The route heads northwest to the town of Glen Hope, where the route has