Square root of 5 one, when traversing the cube "surface" (the shortest distance when traversing through the "inside" of the cube corresponds to the length of the cube diagonal, which is the square root of three times the edge). The number can be algebraically and geometrically related to and , as it is the length of the hypotenuse of a right triangle with catheti measuring and (again, the Pythagorean theorem proves this). Right triangles of such proportions can be found inside a cube: the sides of any triangle defined by the centre point of a cube, one of its vertices, and the middle point
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,