2026/108/1-2 (10)
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DOI: 10.5486/PMD.2026.10316
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pp. 197-200
On a conjecture by Pethő concerning absolute values of roots of generalized Fibonacci polynomials
Authors:
Florian Luca 
and Diego Marques
Abstract:
In this note, we confirm a conjecture raised by Pethő (in 2021), which states that the absolute values of the roots of two distinct generalized Fibonacci polynomials are distinct.
Keywords: $k$-generalized Fibonacci polynomials, size of roots, Galois automorphism, Pisot numbers
Mathematics Subject Classification: 11B39, 12D10