• Euler’s criterion for eleventh power nonresidues

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    • Keywords


      Euler’s criterion; Jacobi sums; cyclotomic numbers; power residues

    • Abstract


      Let $p$ be a prime $\equiv 1\pmod{p}$. If an integer $D$ with $(p,D)=1$ is an eleventh power nonresidue $\pmod{p}$, then $D^{(p-1)/11} \equiv \alpha\, \pmod{p}$ for some eleventh root of unity $\alpha(\not \equiv 1)\,\pmod{p}$. In this paper, we establish an explicit expression for $\alpha$ in terms of a particular solution of certain quadratic partition of $p$. Euler's criterion for eleventh power residues and nonresidues is given with explicit results for $D=2, 7,11$.

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    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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