Given 2 is primitive root (mod p), showing that every non-zero element of Z(p) is expressable as power of [2]...
0
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I'm trying to find out how I would go about showing this:
Given a prime number p >= 2, suppose 2 is a primitive root modulo p.
Show that every non-zero element of Z(p) can be written as a power of [2] (mod p).
Z(p) refers to the congruence class modulo p.
Any ideas?
modular-arithmetic primitive-roots
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
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show 2 more comments
0
$begingroup$
I'm trying to find out how I would go about showing this:
Given a prime number p >= 2, suppose 2 is a primitive root modulo p.
Show that every non-zero element of Z(p) can be written as a power of [2] (mod p).
Z(p) refers to the congruence class modulo p.
Any ideas?
modular-arithmetic primitive-roots
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
$endgroup$
2
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59
|
show 2 more comments
0
0
0
$begingroup$
I'm trying to find out how I would go about showing this:
Given a prime number p >= 2, suppose 2 is a primitive root modulo p.
Show that every non-zero element of Z(p) can be written as a power of [2] (mod p).
Z(p) refers to the congruence class modulo p.
Any ideas?
modular-arithmetic primitive-roots
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
$endgroup$
I'm trying to find out how I would go about showing this:
Given a prime number p >= 2, suppose 2 is a primitive root modulo p.
Show that every non-zero element of Z(p) can be written as a power of [2] (mod p).
Z(p) refers to the congruence class modulo p.
Any ideas?
modular-arithmetic primitive-roots
modular-arithmetic primitive-roots
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
edited Jan 8 at 9:24
Blackb3ard
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
asked Jan 8 at 5:24
Blackb3ardBlackb3ard
11
11
2
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59
|
show 2 more comments
2
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59
2
2
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59
|
show 2 more comments
0
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2
$begingroup$
Isn't it the definition of a primitive root that all the residue classes are its powers? What is your definition of a primitive root?
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:34
$begingroup$
Also, please check our guide to new askers for tips in making your question passable.
$endgroup$
– Jyrki Lahtonen
Jan 8 at 5:35
$begingroup$
"Isn't it the definition of a primitive root that all the residue classes are its powers?" Yes, I think so too. Does it matter?
$endgroup$
– Blackb3ard
Jan 8 at 7:01
$begingroup$
So there is nothing to prove :-)
$endgroup$
– Jyrki Lahtonen
Jan 8 at 8:07
$begingroup$
How about I change the word "prove" to "show" or "verify". Does this better describe my question to you?
$endgroup$
– Blackb3ard
Jan 8 at 8:59