primitive root

Noun

 * 1)  For a given modulus n, a number g such that for every a coprime to n there exists an integer k such that gk ≡ a (mod n); a generator (or primitive element) of the multiplicative group, modulo n, of integers relatively prime to n.

Usage notes

 * Often qualified, as primitive root modulo n.
 * The term is used (only) in number theory, in the context of modular arithmetic, and refers to an integer modulo n (more formally, it refers to a congruence class of integers).
 * The synonyms and  (or generating element) have broader applicability, and refer to an element of a multiplicative group.

Translations

 * Chinese:
 * Mandarin: 原根
 * Finnish: primitiivinen juuri
 * French: racine primitive
 * German: Primitivwurzel
 * Icelandic: frumstæð rót
 * Italian: radice primitiva