Haojie Hong

activity

20222026

collaborators

3 papers

math.NT2026

Monogenity of Fibonacci polynomials and Lucas polynomials

Han Chen, Weizhe Guo, Haojie Hong

We investigate the monogenity of irreducible factors of the Fibonacci polynomials $F_{n} (x)$ and the Lucas polynomials $L_{n} (x)$ . Our main results show that for every odd positive int…

math.NT2023

On big primitive divisors of Fibonacci numbers

Haojie Hong

In this note, we prove that for any given positive integer $κ$ , when $n$ is bigger than a constant explicitly depending on $κ$ , the $n$ -th Fibonacci number has a primitive divisor…

math.NT2022

Stewart's Theorem revisited: suppressing the norm $\pm 1$ hypothesis

Haojie Hong

Let $γ$ be an algebraic number of degree $2$ and not a root of unity. In this note we show that there exists a prime ideal $p$ of $Q (γ)$ satisfying $ν_\mathfrak…

Monogenity of Fibonacci polynomials and Lucas polynomials

On big primitive divisors of Fibonacci numbers

Stewart's Theorem revisited: suppressing the norm ±1 hypothesis

Stewart's Theorem revisited: suppressing the norm $\pm 1$ hypothesis