English Dictionary

primitive root

名詞

(mathematics, number theory) 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.

日本語の意味

【原始根】（数論）ある法 n に対して、n と互いに素な整数全体の乗法群の生成元となる整数。すなわち、与えられた modulus において、その整数 g のべき乗をとることで、n と互いに素な全ての整数を順に表現できる数。

When trying to solve congruences modulo n, identifying a primitive root can reduce many problems to exponent arithmetic.

合同方程式を法 n で解こうとする際、法 n の乗法群の生成元を特定すれば、多くの問題を指数演算に還元できます。

意味（1）

(mathematics, number theory) 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.

There are 𝜙(p-1) incongruent primitive roots of p. The fact that there are so many primitive roots causes no difficulty in the theory of the binomial congruence but has caused considerable confusion in the tabulation of primitive roots.

primitive roots （ plural ）