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 Mar20 awarded Curious Sep24 awarded Autobiographer Jul30 awarded Yearling May13 comment The number of subgroup in $\mathbb{Z}_N^*$ no, it's not I want, e.g. in the $\mathbb{Z}_N^*$, there is a subgroup $\mathbb{G}$ and $\mathbb{G} \subset \mathbb{Z}_N^*$. Now I suppose the order of $\mathbb{G}$ is $p$. Then, what I want to know is how many different subgroups with order $p$ in $\mathbb{Z}_N^*$. things like that .. May13 asked The number of subgroup in $\mathbb{Z}_N^*$ Nov14 answered Does the $\gcd(2n-1,2n+1)=1?$ Oct15 awarded Commentator Sep18 comment A problem about the discrete logarithm maybe we could use some tricks of choosing some special $x$ that can reveal some information of $b$. Sep18 answered How to solve $e^x = 2$ Sep18 asked A problem about the discrete logarithm Sep16 comment Let $G$ be a group with order $p$ a prime number. Show $G$ is cyclic. thanks i have corrected as you've said Sep16 revised Let $G$ be a group with order $p$ a prime number. Show $G$ is cyclic. added 15 characters in body Sep16 answered Let $G$ be a group with order $p$ a prime number. Show $G$ is cyclic. Sep16 awarded Teacher Sep15 answered Proving that identity element is the only element of a group Sep14 comment how to find generator in $F_2[x]/(f(x))$? @JyrkiLahtonen why "$m(m(x))$ is divisible by $f(x)$"? Sep14 revised how to find generator in $F_2[x]/(f(x))$? edited title Sep14 comment how to find generator in $F_2[x]/(f(x))$? @JyrkiLahtonen let $\xi$ be a generator in $F_{2^n}$, $m(x)$ is the characteristic polynomial of $\xi$. there is a map : $\xi \to m(x)$, considering $\xi^2 \to m(x)^2$,$\xi^3 \to m(x)^3$,...,$\xi^{2^n-1} \to m(x)^{2^n-1}$. Because $\xi$ is generator so $\xi,...,\xi^{2^n-1}$ are all pairwise different and so do $m(x),...,m(x)^{2^n-1}$. now $\{m(x),...,m(x)^{2^n-1}\} \pmod{f(x)} \in F_2[x]/(f(x))$, they are different from each other Sep14 comment how to find generator in $F_2[x]/(f(x))$? @JyrkiLahtonen can i get a generator in $F_2[x]/(f(x))$ by $m(x)\pmod{f(x)}$? Sep12 comment how to find generator in $F_2[x]/(f(x))$? if a primitive polynomial ( degree$=n$ )is found, then it's roots are primitive elements. considering one of these roots $\xi$, $\varphi(\xi)=k(x)$, then a $k(x)$ is found. is this feasible?