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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
1729 is composite, the squarefree product of three prime numbers 7 × 13 × 19. [1] It has as factors 1, 7, 13, 19, 91, 133, 247, and 1729. [2] It is the third Carmichael number, [3] and the first Chernick–Carmichael number. [a] Furthermore, it is the first in the family of absolute Euler pseudoprimes, a subset of Carmichael numbers.
In other cases, the coefficients may be complex numbers, and the function is a complex function that has the set of the complex numbers as its codomain, even when the domain is restricted to the real numbers. Setting f(x) = 0 produces a cubic equation of the form + + + =,
Here is an angle in the unit circle; taking 1 / 3 of that angle corresponds to taking a cube root of a complex number; adding −k 2 π / 3 for k = 1, 2 finds the other cube roots; and multiplying the cosines of these resulting angles by corrects for scale.
Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of “to the power of 4”. The sequence of fourth powers of integers, known as biquadrates or tesseractic numbers, 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: