Mixing
Issue with Root of Unity Proof [duplicate]
$begingroup$
This question already has an answer here:
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]
2 answers
Cyclic Group Generators of Order $n$
5 answers
I need some help with a proof:
Let $gcd(k,n)=1, w_n = e^{2*pi*i/n}$ and $w_n^k = e^{2*pi*i*k/n}$. Show that the equation $ <w_n> = <w_n^k>$ holds, where $<x>$ = {$x^n|n in N_0 $}
Is it necessary to show, that $w_n^k$ is primitive, if $gcd(k,n)=1$ holds?
discrete-mathematics complex-numbers
asked Jan 20 at 20:05
Jack MowJack Mow
4
$endgroup$
marked as duplicate by Dietrich Burde, Lord Shark the Unknown, metamorphy, José Carlos Santos, Jose Arnaldo Bebita Dris Jan 21 at 11:49
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]
2 answers
Cyclic Group Generators of Order $n$
5 answers
I need some help with a proof:
Let $gcd(k,n)=1, w_n = e^{2*pi*i/n}$ and $w_n^k = e^{2*pi*i*k/n}$. Show that the equation $ <w_n> = <w_n^k>$ holds, where $<x>$ = {$x^n|n in N_0 $}
Is it necessary to show, that $w_n^k$ is primitive, if $gcd(k,n)=1$ holds?
discrete-mathematics complex-numbers
asked Jan 20 at 20:05
Jack MowJack Mow
4
$endgroup$
marked as duplicate by Dietrich Burde, Lord Shark the Unknown, metamorphy, José Carlos Santos, Jose Arnaldo Bebita Dris Jan 21 at 11:49
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29
add a comment |
$begingroup$
This question already has an answer here:
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]
2 answers
Cyclic Group Generators of Order $n$
5 answers
I need some help with a proof:
Let $gcd(k,n)=1, w_n = e^{2*pi*i/n}$ and $w_n^k = e^{2*pi*i*k/n}$. Show that the equation $ <w_n> = <w_n^k>$ holds, where $<x>$ = {$x^n|n in N_0 $}
Is it necessary to show, that $w_n^k$ is primitive, if $gcd(k,n)=1$ holds?
discrete-mathematics complex-numbers
asked Jan 20 at 20:05
Jack MowJack Mow
4
$endgroup$
This question already has an answer here:
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]
2 answers
Cyclic Group Generators of Order $n$
5 answers
I need some help with a proof:
Let $gcd(k,n)=1, w_n = e^{2*pi*i/n}$ and $w_n^k = e^{2*pi*i*k/n}$. Show that the equation $ <w_n> = <w_n^k>$ holds, where $<x>$ = {$x^n|n in N_0 $}
Is it necessary to show, that $w_n^k$ is primitive, if $gcd(k,n)=1$ holds?
This question already has an answer here:
If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]
2 answers
Cyclic Group Generators of Order $n$
5 answers
discrete-mathematics complex-numbers
discrete-mathematics complex-numbers
asked Jan 20 at 20:05
Jack MowJack Mow
4
asked Jan 20 at 20:05
Jack MowJack Mow
4
asked Jan 20 at 20:05
Jack MowJack Mow
4
asked Jan 20 at 20:05
Jack MowJack Mow
4
asked Jan 20 at 20:05
Jack MowJack Mow
4
4
marked as duplicate by Dietrich Burde, Lord Shark the Unknown, metamorphy, José Carlos Santos, Jose Arnaldo Bebita Dris Jan 21 at 11:49
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Dietrich Burde, Lord Shark the Unknown, metamorphy, José Carlos Santos, Jose Arnaldo Bebita Dris Jan 21 at 11:49
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29
add a comment |
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29
add a comment |
0
active
oldest
votes
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$.
$endgroup$
– Dietrich Burde
Jan 20 at 20:09
$begingroup$
Welcome the Mathematics Stack Exchange community. A quick tour of the site will help you get the most of your time here.
$endgroup$
– dantopa
Jan 20 at 20:29