Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$? [closed]
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Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$ (since $1$ is a primitive root of $2$ but $1$ is not a primitive root of $4$)?
Are there other examples?
elementary-number-theory prime-numbers primitive-roots
edited Nov 17 at 23:00
Mr. Brooks
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, amWhy Nov 18 at 11:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Scientifica, Parcly Taxel, max_zorn, jgon, amWhy
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add a comment |
up vote
3
down vote
favorite
Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$ (since $1$ is a primitive root of $2$ but $1$ is not a primitive root of $4$)?
Are there other examples?
elementary-number-theory prime-numbers primitive-roots
edited Nov 17 at 23:00
Mr. Brooks
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, amWhy Nov 18 at 11:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Scientifica, Parcly Taxel, max_zorn, jgon, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$ (since $1$ is a primitive root of $2$ but $1$ is not a primitive root of $4$)?
Are there other examples?
elementary-number-theory prime-numbers primitive-roots
edited Nov 17 at 23:00
Mr. Brooks
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$ (since $1$ is a primitive root of $2$ but $1$ is not a primitive root of $4$)?
Are there other examples?
elementary-number-theory prime-numbers primitive-roots
elementary-number-theory prime-numbers primitive-roots
edited Nov 17 at 23:00
Mr. Brooks
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
edited Nov 17 at 23:00
Mr. Brooks
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
edited Nov 17 at 23:00
Mr. Brooks
27311237
edited Nov 17 at 23:00
Mr. Brooks
27311237
edited Nov 17 at 23:00
Mr. Brooks
27311237
27311237
asked Nov 17 at 18:04
Joseph Jeong
161
asked Nov 17 at 18:04
Joseph Jeong
161
asked Nov 17 at 18:04
Joseph Jeong
161
161
closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, amWhy Nov 18 at 11:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Scientifica, Parcly Taxel, max_zorn, jgon, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, amWhy Nov 18 at 11:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Scientifica, Parcly Taxel, max_zorn, jgon, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42
add a comment |
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42
add a comment |
1 Answer
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If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
$p$ but not modulo $p^2$.
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
$p$ but not modulo $p^2$.
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
add a comment |
up vote
0
down vote
If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
$p$ but not modulo $p^2$.
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
add a comment |
up vote
0
down vote
up vote
0
down vote
If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
$p$ but not modulo $p^2$.
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
$p$ but not modulo $p^2$.
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
answered Nov 17 at 18:05
Lord Shark the Unknown
98.1k958131
98.1k958131
add a comment |
add a comment |
math.stackexchange.com/questions/227199/…
– lab bhattacharjee
Nov 17 at 18:07
See oeis.org/A055578 and oeis.org/A060503
– lhf
Nov 18 at 1:42