Chen-kai Ren

activity

20232025

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Showing 2024Show all

3 papers · 1 filter

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…

math.NT2024

On some determinants arising from quadratic residues

Chen-Kai Ren, Zhi-Wei Sun

Let $p > 3$ be a prime, and let $d \in Z$ with $p ∤ d$ . For the determinants $$S_m(d,p)=\det\left[(i^2+dj^2)^{m}\right]_{1\leqslant i,j \leqslant (p-1)/2}\ \ \left(\frac{p-1…