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







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closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, amWhy Nov 18 at 11:18


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  • 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

















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







share|cite|improve this 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















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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













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share|cite|improve this question








edited Nov 17 at 23:00









Mr. Brooks

27311237




27311237










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




















  • 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












1 Answer
1






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up vote
0
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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 $p^2$.






share|cite|improve this answer




























    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 $p^2$.






    share|cite|improve this answer

























      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 $p^2$.






      share|cite|improve this answer























        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 $p^2$.






        share|cite|improve this answer












        If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo
        $p$ but not modulo $p^2$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 17 at 18:05









        Lord Shark the Unknown

        98.1k958131




        98.1k958131















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