Divisibility properties of factors of the discriminant of generalized Fibonacci numbers

2020/03/14 by Yao-Qiang Li, Li, Yao-Qiang
Physics and Astronomy · Mathematics · Materials Science · #Advanced Mathematical Theories and Applications #Advanced Mathematical Identities #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/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≥0 defined by G₀=0, G₁=1 and G_n=pG_n-1+qG_n-2 for n≥2, where p,q are given integers. As corollaries, we give some divisibility properties on some well known sequences.

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