Weilin Zhang

activity

20232026

collaborators

8 papers

math.NT2026

Critical Pairs for Mixed Restricted Sumsets in Prime Fields

Weilin Zhang, Hongjian Li

Let $p$ be an odd prime and let $A, B \subseteq F_{p}$ be nonempty and distinct, with $∣ A ∣ \geq ∣ B ∣$ . We give a complete classification of the pairs for which the mixed restricte…

math.NT2026

Reducibility of $r x^{m} + p^{e} f (x)$ for Large Primes $p$

Weilin Zhang, Hongjian Li

We study the reducibility over $Q$ of $F_{p, e} (x) = r x^{m} + p^{e} f (x)$ , where $r \in Z ∖ {0}$ , $f \in Z [x]$ , and $0 \leq m < n := deg f$ , for primes $p…

math.NT2026

The Fermat-Type Matrix Equation over $GL_{2} (Z)$

Hongjian Li, Weilin Zhang

We determine the complete ordered solution set of the Fermat-type matrix equation $X^{n} + Y^{n} = Z^{n}$ in $GL_{2} (Z)$ for every integer $n \geq 3$ , expressed in terms of simu…

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…

math.NT2023

A note on an irreducible class of polynomials over integers

Zhang Weilin, Yuan Pingzhi

In this note, we prove an irreducibility criterion for the polynomial of the form $f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{m} x^{m} + p^{u} \in Z [x]$ , where $p$ is…

Critical Pairs for Mixed Restricted Sumsets in Prime Fields

Reducibility of rxm+pef(x) for Large Primes p

The Fermat-Type Matrix Equation over GL2​(Z)

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

A note on an irreducible class of polynomials over integers

Reducibility of $r x^{m} + p^{e} f (x)$ for Large Primes $p$

The Fermat-Type Matrix Equation over $GL_{2} (Z)$

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

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