Chen-kai Ren

collaborators

3 papers

math.NT2025

Evaluation of a determinant involving Legendre symbols

Chen-Kai Ren, Zhi-Wei Sun

Let $p > 3$ be a prime, and let $(\frac{\cdot}{p})$ be the Legendre symbol. Let $A_{p} (x)$ denote the matrix $[x + a_{ij}]_{1 ⩽ i, j ⩽ (p - 1) /2}$ , where $$ a_{ij}=\begin{cases}…

math.NT2024

On some determinant conjectures

Ze-Hua Zhu, Chen-Kai Ren

Let $p$ be a prime and $c, d \in Z$ . Sun introduced the determinant $D_{p}^{-} (c, d) := det [(i^{2} + c ij + d j^{2})^{p - 2}]_{1 < i, j < p - 1}$ for $p > 3$ . In this paper, we confirm three conjecture…

math.NT2024

On certain determinants and the square root of some determinants involving Legendre Symbols

Chen-kai Ren, Xin-qi Luo

Let $p > 3$ be a prime and $(\frac{.}{p})$ be the Legendre symbol. For any integer $d$ with $p ∤ d$ and any positive integer $m$ , Sun introduced the determinants $$T_m(d,p)=\det\l…