Unit cube unit hypercube of "n" dimensions is formula_1, the square root of "n" and the (Euclidean) length of the vector (1,1,1...1,1) in "n"-dimensional space. Unit cube A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units. The term "unit cube" or unit hypercube is also used for hypercubes, or "cubes" in "n"-dimensional spaces, for values of "n" other than 3 and edge length 1. Sometimes the term "unit cube" refers in specific
Root of unity modulo n it is not a primitive root, then there would be some divisor ℓ of "k", with formula_57. In order to exclude this possibility, one has only to check for a few ℓ's equal "k" divided by a prime. That is, what needs to be checked is: Among the primitive "k"-th roots of unity, the primitive formula_23-th roots are most frequent. It is thus recommended to try some integers for being a primitive formula_23-th root, what will succeed quickly. For a primitive formula_23-th root "x", the number formula_30 is a primitive formula_25-th root of unity. If "k" does not divide formula_23,