Last Updated
：2025/11/28
primitive root
Noun
Japanese Meaning
【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。
（ plural ）
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(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.
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primitive root
When trying to solve congruences modulo n, identifying a primitive root can reduce many problems to exponent arithmetic.
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When trying to solve congruences modulo n, identifying a primitive root can reduce many problems to exponent arithmetic.
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