• Euler’s criterion for eleventh power nonresidues

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/129/03/0041

• # 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 $D=2, 7,11$.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019