Consecutive Quadratic Residues And Quadratic Nonresidue Modulo p

2020/11/17 by N. A. Carella, Carella, N. A.
Computer Science · Mathematics · #2020: Primary 11A15 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #General Mathematics (math.GM) #Limits and Structures in Graph Theory #Secondary 11L40

paper · pdf · doi:10.48550/arxiv.2011.11054

openalex publication_date 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a large prime, and let k≪ log p. A new proof of the existence of any pattern of k consecutive quadratic residues and quadratic nonresidues is introduced in this note. Further, an application to the least quadratic nonresidues n_p modulo p shows that n_p≪ (log p)(log log p).

Citations

• Pólya-Vinogradov and the least quadratic nonresidue

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• Vinogradov's Conjecture and Beyond
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