Haojie Hong

activity

20212026

most citedUniform explicit Stewart's theorem on prime factors of linear recurrences

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 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…

math.NT2021

Big prime factors in orders of elliptic curves over finite fields

Yuri Bilu, Haojie Hong, Florian Luca

Let $E$ be an elliptic curve over the finite field $F_{q}$ . We prove that, when $n$ is a sufficiently large positive integer, $# E (F_{q^{n}})$ has a prime factor exceed…

math.NT2021★ 1 cited

Uniform explicit Stewart's theorem on prime factors of linear recurrences

Yuri Bilu, Haojie Hong, Sanoli Gun

Stewart (2013) proved that the biggest prime divisor of the $n$ th term of a Lucas sequence of integers grows quicker than $n$ , answering famous questions of Erdős and Schinzel. In…

Monogenity of Fibonacci polynomials and Lucas polynomials

On big primitive divisors of Fibonacci numbers

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

Big prime factors in orders of elliptic curves over finite fields

Uniform explicit Stewart's theorem on prime factors of linear recurrences

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