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arXiv · 2606.15438

Least Consecutive Pair of Quadratic Nonresidues

N. A. Carella
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Abstract

Let $p>1$ be a large prime number and let $x=O((\log p)^2(\log\log p)^3$ be a real number. It is proved that the least consecutive pair of quadratic nonresidues $u\ne\pm1, v^2$ and $u+1$ satisfies the upper bound $u\ll x$ in the prime field $\mathbb{F}_p$.

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N. A. Carella. 2026-06-13. Least Consecutive Pair of Quadratic Nonresidues. https://arxiv.org/abs/2606.15438

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