Ads
related to: primitive root table
Search results
Results From The WOW.Com Content Network
That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which g k ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n.
The table below lists the shortest decomposition (among those, the lexicographically first is chosen – this guarantees isomorphic groups are listed with the same decompositions). The generating set is also chosen to be as short as possible, and for n with primitive root, the smallest primitive root modulo n is listed.
Jacobi's original tables use 10 or –10 or a number with a small power of this form as the primitive root whenever possible, while the second edition uses the smallest possible positive primitive root (Fletcher 1958). The term "canon arithmeticus" is occasionally used to mean any table of indices and powers of primitive roots.
For n = 1, the cyclotomic polynomial is Φ 1 (x) = x − 1 Therefore, the only primitive first root of unity is 1, which is a non-primitive n th root of unity for every n > 1. As Φ 2 (x) = x + 1, the only primitive second (square) root of unity is −1, which is also a non-primitive n th root of unity for every even n > 2.
Toggle the table of contents. Dirichlet character. 18 languages. ... −1 is a primitive root mod 4 ...
Toggle the table of contents. Primitive root. 4 languages. Español; Français; ... In mathematics, a primitive root may mean: Primitive root modulo n in modular ...