Xin Luo

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20142023

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math.NT2023

On an inverse problem for restricted sumsets

Xin-Qi Luo, Zhi-Wei Sun

Let $n$ be a positive integer, and let $A$ be a set of $k \geq 2 n - 1$ integers. For the restricted sumset $$ S_n(A)=\{a_1+\cdots +a_n:\ a_1,\ldots,a_n\in A,\ \text{and}\ a_i^2\neq a_j…

math.NT2022

Legendre symbols related to certain determinants

Xin-Qi Luo, Zhi-Wei Sun

Let $p$ be an odd prime. For $b, c \in Z$ , Sun introduced the determinant $D_{p} (b, c) = (i^{2} + bij + c j^{2})^{p - 2}_{1 ⩽ i, j ⩽ p - 1},$ and investigated the L…