Phrase guide

primitive root

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

7 source translations are retained for this English entry.

  • Chinese Mandarin: 原根 (yuángēn) — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • Finnish: primitiivinen juuri — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • French: racine primitive — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • German: Primitivwurzel — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • Icelandic: frumstæð rót — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • Italian: radice primitiva — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element
  • Polish: pierwiastek pierwotny — number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element