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Let $q\geq 1$ be any integer and let $\unicode[STIX]{x1D716}\in [\frac{1}{11},\frac{1}{2})$ be a given real number. We prove that for all primes $p$ satisfying

$$\begin{eqnarray}p\equiv 1\!\!\!\!\hspace{0.6em}({\rm mod}\hspace{0.2em}q),\quad \log \log p>\frac{2\log 6.83}{1-2\unicode[STIX]{x1D716}}\quad \text{and}\quad \frac{\unicode[STIX]{x1D719}(p-1)}{p-1}\leq \frac{1}{2}-\unicode[STIX]{x1D716},\end{eqnarray}$$

there exists a quadratic nonresidue

$g$ which is not a primitive root modulo

$p$ such that

$\text{gcd}(g,(p-1)/q)=1$.

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QUADRATIC NONRESIDUES AND NONPRIMITIVE ROOTS SATISFYING A COPRIMALITY CONDITION

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11 - Neurodegeneration models inDrosophila

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3 results

QUADRATIC NONRESIDUES AND NONPRIMITIVE ROOTS SATISFYING A COPRIMALITY CONDITION

Contributors

11 - Neurodegeneration models inDrosophila