Mathematics > General Mathematics
arXiv:2606.15438 (math)
[Submitted on 13 Jun 2026]
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 $\mathbb{F}_p$.
| Comments: | Eighteen Pages. Keywords: Quadratic nonresidue mod $p$; Least prime quadratic nonresidue; Complexity theory; Finite field |
| Subjects: | General Mathematics (math.GM) |
| MSC classes: | Primary 11A07, 11A15, Secondary 11L07 |
| Cite as: | arXiv:2606.15438 [math.GM] |
| (or arXiv:2606.15438v1 [math.GM] for this version) | |
| https://doi.org/10.48550/arXiv.2606.15438 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: N. A. Carella [view email]
[v1]
Sat, 13 Jun 2026 19:05:15 UTC (16 KB)
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