Divisibility properties of factors of the discriminant of generalized Fibonacci numbers

Yao-Qiang Li

paper

Divisibility properties of factors of the discriminant of generalized Fibonacci numbers

arXiv:2003.06643

Abstract

We study some divisibility properties related to the factors of the discriminant of the characteristic polynomial of generalized Fibonacci sequences $(G_{n})_{n \geq 0}$ defined by $G_{0} = 0$ , $G_{1} = 1$ and $G_{n} = p G_{n - 1} + q G_{n - 2}$ for $n \geq 2$ , where $p, q$ are given integers. As corollaries, we give some divisibility properties on some well known sequences.