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Because of the factorization (2n + 1)(n 2 + n + 1), it is impossible for a centered cube number to be a prime number. [3] The only centered cube numbers which are also the square numbers are 1 and 9, [4] [5] which can be shown by solving x 2 = y 3 + 3y, the only integer solutions being (x,y) from {(0,0), (1,2), (3,6), (12,42)}, By substituting a=(x-1)/2 and b=y/2, we obtain x^2=2y^3+3y^2+3y+1.
The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number, is
A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four ...
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. [1] The most famous taxicab number is 1729 = Ta(2) = 1 3 + 12 3 = 9 3 + 10 3 , also known as the Hardy-Ramanujan number.
In geometry, a 10-cube is a ten-dimensional hypercube. It has 1024 vertices, 5120 edges, 11520 square faces, 15360 cubic cells, 13440 tesseract 4-faces, 8064 5-cube 5-faces, 3360 6-cube 6-faces, 960 7-cube 7-faces, 180 8-cube 8-faces, and 20 9-cube 9-faces. It can be named by its Schläfli symbol {4,3 8}, being composed of 3 9-cubes around
Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units. The Bedlam cube is a 4×4×4 sided cube puzzle consisting of twelve pentacubes and one tetracube. The Diabolical cube is a puzzle of six polycubes that can be assembled together to form a single 3×3×3 cube.