Weilin Zhang

collaborators

4 papers

math.NT2026

The Matrix Pythagorean Equation over $GL_{2} (Z)$

Hongjian Li, Weilin Zhang

In this paper, we study the ordered solutions of the matrix Pythagorean equation $X^{2} + Y^{2} = Z^{2}$ over $GL_{2} (Z)$ . Exploiting the independent sign symmetry of the eq…

math.NT2026

A Multiplicative Fourier Proof of the Length-Four Index Conjecture

Hongjian Li, Pingzhi Yuan, Shijie Yuan +1

Let $C_{n}$ be a cyclic group of order $n$ . We prove that if $(n, 6) = 1$ , then every minimal zero-sum sequence of length four over $C_{n}$ has index one, thereby resolving the length-fou…

math.NT2025

On the Elementary Symmetric Functions of ${1, 1/2, \dots, 1/ n} \ {1/ i}$

Weilin Zhang, Hongjian Li, Sunben Chiu +1

In 1946, P. Erdős and I. Niven proved that there are only finitely many positive integers $n$ for which one or more of the elementary symmetric functions of $1, 1/2$ , $\cdots, 1 /…

math.NT2025

On the representation of rational numbers via Euler's totient function

Weilin Zhang, Fengyuan Chen, Hongjian Li +1

Let $b > 1$ be an odd positive integer and $k, l \in N$ . In this paper, we show that every positive rational number can be written as $φ (m^{2}) / (φ (n^{2}))^{b}$ and $φ(k(m^{2…

The Matrix Pythagorean Equation over GL2​(Z)

A Multiplicative Fourier Proof of the Length-Four Index Conjecture

On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}

On the representation of rational numbers via Euler's totient function

The Matrix Pythagorean Equation over $GL_{2} (Z)$

On the Elementary Symmetric Functions of ${1, 1/2, \dots, 1/ n} \ {1/ i}$