Jacobi symbol of sum of two squares

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Say we have $x=a^2+b^2$. Are there any results regarding the Jacobi symbol $(fracxn)$, where $n=p*q$?
Having $x'=a^2+c^2$, is there any connection between the Jacobi symbols $(fracxn)$ and $(fracx'n)$?




number-theory prime-numbers jacobi-symbol




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  • 1




    I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
    – Peter
    Aug 2 at 8:13






  • 1




    Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
    – Peter Taylor
    Aug 2 at 10:08










  • It's related to an encryption scheme.
    – saa
    Aug 2 at 11:19














up vote
0
down vote

favorite












Say we have $x=a^2+b^2$. Are there any results regarding the Jacobi symbol $(fracxn)$, where $n=p*q$?
Having $x'=a^2+c^2$, is there any connection between the Jacobi symbols $(fracxn)$ and $(fracx'n)$?




number-theory prime-numbers jacobi-symbol




share|cite|improve this question















  • 1




    I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
    – Peter
    Aug 2 at 8:13






  • 1




    Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
    – Peter Taylor
    Aug 2 at 10:08










  • It's related to an encryption scheme.
    – saa
    Aug 2 at 11:19












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Say we have $x=a^2+b^2$. Are there any results regarding the Jacobi symbol $(fracxn)$, where $n=p*q$?
Having $x'=a^2+c^2$, is there any connection between the Jacobi symbols $(fracxn)$ and $(fracx'n)$?




number-theory prime-numbers jacobi-symbol




share|cite|improve this question











Say we have $x=a^2+b^2$. Are there any results regarding the Jacobi symbol $(fracxn)$, where $n=p*q$?
Having $x'=a^2+c^2$, is there any connection between the Jacobi symbols $(fracxn)$ and $(fracx'n)$?





number-theory prime-numbers jacobi-symbol





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 2 at 8:08









saa

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213







  • 1




    I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
    – Peter
    Aug 2 at 8:13






  • 1




    Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
    – Peter Taylor
    Aug 2 at 10:08










  • It's related to an encryption scheme.
    – saa
    Aug 2 at 11:19












  • 1




    I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
    – Peter
    Aug 2 at 8:13






  • 1




    Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
    – Peter Taylor
    Aug 2 at 10:08










  • It's related to an encryption scheme.
    – saa
    Aug 2 at 11:19







1




1




I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
– Peter
Aug 2 at 8:13




I think the answer to both questions is "no" , even if $p$ and $q$ are distinct primes (which I assume)
– Peter
Aug 2 at 8:13




1




1




Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
– Peter Taylor
Aug 2 at 10:08




Is there any particular reason for wanting $n$ to be a semiprime? Since the Jacobi symbol is just the product of Legendre symbols, it seems to me to make more sense to ask about $(fracxp)$ where $p$ is prime.
– Peter Taylor
Aug 2 at 10:08












It's related to an encryption scheme.
– saa
Aug 2 at 11:19




It's related to an encryption scheme.
– saa
Aug 2 at 11:19















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