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Monogenity of Fibonacci polynomials and Lucas polynomials
Han Chen, Weizhe Guo, Haojie Hong
We investigate the monogenity of irreducible factors of the Fibonacci polynomials and the Lucas polynomials . Our main results show that for every odd positive int…
On big primitive divisors of Fibonacci numbers
Haojie Hong
In this note, we prove that for any given positive integer , when is bigger than a constant explicitly depending on , the -th Fibonacci number has a primitive divisor…
Stewart's Theorem revisited: suppressing the norm hypothesis
Haojie Hong
Let be an algebraic number of degree and not a root of unity. In this note we show that there exists a prime ideal of satisfying $ν_\mathfrak…
Big prime factors in orders of elliptic curves over finite fields
Yuri Bilu, Haojie Hong, Florian Luca
Let be an elliptic curve over the finite field . We prove that, when is a sufficiently large positive integer, has a prime factor exceed…
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 th term of a Lucas sequence of integers grows quicker than , answering famous questions of Erdős and Schinzel. In…