Primitive root

Primitive root

In mathematics, a primitive root may mean either

* a primitive root modulo n in modular arithmetic, or
* a primitive n-th root of unity amongst the solutions of "xn" = 1 in a field.

See also: primitive element.


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  • Primitive root modulo n — In modular arithmetic, a branch of number theory, a primitive root modulo n is any number g with the property that any number coprime to n is congruent to a power of g (mod n ). That is, if g is a primitive root (mod n ) and gcd( a , n ) = 1,… …   Wikipedia

  • Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially …   Wikipedia

  • Primitive element (finite field) — In field theory, a branch of mathematics, a primitive element of a finite field GF ( q ) is a generator of the multiplicative group of the field, which is necessarily cyclic. The minimal polynomial of a primitive element is a primitive polynomial …   Wikipedia

  • Primitive element — In mathematics, the term primitive element can mean: * Primitive root modulo n , in number theory * Primitive element (field theory), an element that generates a given field extension * Primitive element (finite field), an element that generates… …   Wikipedia

  • Root — Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion, or… …   The Collaborative International Dictionary of English

  • Root and branch — Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion …   The Collaborative International Dictionary of English

  • Root barnacle — Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion …   The Collaborative International Dictionary of English

  • Root hair — Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion …   The Collaborative International Dictionary of English

  • Root leaf — Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion …   The Collaborative International Dictionary of English

  • Root louse — Root Root, n. [Icel. r[=o]t (for vr[=o]t); akin to E. wort, and perhaps to root to turn up the earth. See {Wort}.] 1. (Bot.) (a) The underground portion of a plant, whether a true root or a tuber, a bulb or rootstock, as in the potato, the onion …   The Collaborative International Dictionary of English

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