P. S. Kosobutskyy

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 1, Pages 172-178

DOI: 10.7546/nntdm.2020.26.1.172-178

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## Details

### Authors and affiliations

P. S. Kosobutskyy

*Department of Computer-Aided Design
Lviv Polytechnic National University
S. Bandery 12 St., Lviv, 79646, Ukraine*

### Abstract

In this paper it is shown that there is a plurality of irrational values of the roots of a quadratic equation with equal modulus coefficients |*p*| = |*q*| ≠ 1 having properties of the numbers of Phidias *φ = 0.*61803… and Ф = 1.61803… It is shown that it is also possible to construct a set of sequences possessing the basic properties of the Fibonacci and Lucas sequences.

### Keywords

- Golden ratio
- Quadratic irrationality
- Roots of quadratic equation

### 2010 Mathematics Subject Classification

- 11B37
- 11B39

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## Cite this paper

Kosobutskyy, P. S. (2020). Phidias numbers as a basis for Fibonacci analogues. Notes on Number Theory and Discrete Mathematics, 26(1), 172-178, doi: 10.7546/nntdm.2020.26.1.172-178.