How to prove that one of $2,3,6$ is a square modulo every prime $p$? [duplicate]












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  • When is 6 a square in Zp

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How to prove that one of $2,3,6$ is a square modulo every prime $p$?



I am thinking in terms of quadratic reciprocity but not getting any clue.






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marked as duplicate by Bill Dubuque elementary-number-theory
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 Feb 1 at 5:09


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$begingroup$



This question already has an answer here:




  • When is 6 a square in Zp

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How to prove that one of $2,3,6$ is a square modulo every prime $p$?



I am thinking in terms of quadratic reciprocity but not getting any clue.






number-theory elementary-number-theory algebraic-number-theory







share|cite|improve this question











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marked as duplicate by Bill Dubuque elementary-number-theory
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1





$begingroup$



This question already has an answer here:




  • When is 6 a square in Zp

    1 answer




How to prove that one of $2,3,6$ is a square modulo every prime $p$?



I am thinking in terms of quadratic reciprocity but not getting any clue.






number-theory elementary-number-theory algebraic-number-theory







share|cite|improve this question











$endgroup$





This question already has an answer here:




  • When is 6 a square in Zp

    1 answer




How to prove that one of $2,3,6$ is a square modulo every prime $p$?



I am thinking in terms of quadratic reciprocity but not getting any clue.





This question already has an answer here:




  • When is 6 a square in Zp

    1 answer







number-theory elementary-number-theory algebraic-number-theory




number-theory elementary-number-theory algebraic-number-theory






share|cite|improve this question















share|cite|improve this question













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edited Feb 1 at 5:15









YuiTo Cheng

2,3244937




2,3244937










asked Feb 1 at 4:46









GimgimGimgim

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marked as duplicate by Bill Dubuque elementary-number-theory
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 Feb 1 at 5:09


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marked as duplicate by Bill Dubuque elementary-number-theory
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 Feb 1 at 5:09


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.














  • $begingroup$
    See also this answer
    $endgroup$
    – Bill Dubuque
    Feb 1 at 5:05




















  • $begingroup$
    See also this answer
    $endgroup$
    – Bill Dubuque
    Feb 1 at 5:05


















$begingroup$
See also this answer
$endgroup$
– Bill Dubuque
Feb 1 at 5:05






$begingroup$
See also this answer
$endgroup$
– Bill Dubuque
Feb 1 at 5:05












1 Answer
1






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3












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what is
$$ (2|p) (3|p)(6|p) ; ? $$






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  • $begingroup$
    Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
    $endgroup$
    – Gimgim
    Feb 1 at 4:55


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

what is
$$ (2|p) (3|p)(6|p) ; ? $$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
    $endgroup$
    – Gimgim
    Feb 1 at 4:55
















3












$begingroup$

what is
$$ (2|p) (3|p)(6|p) ; ? $$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
    $endgroup$
    – Gimgim
    Feb 1 at 4:55














3












3








3





$begingroup$

what is
$$ (2|p) (3|p)(6|p) ; ? $$






share|cite|improve this answer









$endgroup$



what is
$$ (2|p) (3|p)(6|p) ; ? $$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Feb 1 at 4:50









Will JagyWill Jagy

104k5103202




104k5103202












  • $begingroup$
    Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
    $endgroup$
    – Gimgim
    Feb 1 at 4:55


















  • $begingroup$
    Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
    $endgroup$
    – Gimgim
    Feb 1 at 4:55
















$begingroup$
Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
$endgroup$
– Gimgim
Feb 1 at 4:55




$begingroup$
Ohh ok $(6|p)=(2|p)(3|p)$ if $p neq 2,3$ then it is always $1$. Thanks
$endgroup$
– Gimgim
Feb 1 at 4:55



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