A century problem related to the Legendre symbol modulo p

2025/06/03 by Wenpeng Zhang, Zhang, Wenpeng · 1 voice
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Historical Astronomy and Related Studies #History and Overview (math.HO) #History and Theory of Mathematics #Number Theory (math.NT) #math.HO #math.NT

paper · pdf · doi:10.48550/arxiv.2506.02434

openalex publication_date 2025/06/03 · arxiv published 2025/06/03 · openalex created_date 2025/10/14 · arxiv updated 2026/03/18 · openalex updated_date 2026/07/30

Abstract

The main purpose of this paper is using a very simple constructive method to study an old number theory problem related to the Legendre symbol modulo p, and completely solved it. The proving method of the result is purely elementary and has been desired in the literature at least since 1927.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Discussions

• Wenpeng Zhang: An old number theory problem related to the Legendre symbol https://arxiv.org/abs/2506.02434 https://arxiv.org/pdf/2506.02434 https://arxiv.org/html/2506.02434 [bsky, 0 points, 1 comments]

Related

• Some interesting number theory problems
• Legendre's conjecture. Theorem on existence of a prime number between m² and (m+1)²
• Legendre Symbol of ∏ f(i,j) over 0<i<j<p/2, p\nmid f(i,j)
• Long nonnegative sums of Legendre symbols
• The Least Number with Prescribed Legendre Symbols