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Last edited by hbghlyj 2024-10-19 09:55$ℤ/12$的不可约元:4,8
$ℤ/36$的不可约元:4,8,9,12,16,18,20,24,27,28
一般地,$a\bmod n$为不可约元,若$\gcd(a,n)=p$,对某个素数$p$使$p^2$整除$n$.
Prime and irreducible elements of the ring of integers modulo n, by Jafari and Madadi
整数mod n不可约元个数\[F(n)=\sum_{p^2\,|\,n} \varphi \left( \frac np\right)\]例如$F(12)=φ(6)=2,F(36)=φ(18)+φ(12)=6+4=10$ |
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