Perron numbers that satisfy Fermat’s equation

Pietro Paparella
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 119—122
DOI: 10.7546/nntdm.2021.27.3.119-122
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Authors and affiliations

Pietro Paparella
Division of Engineering and Mathematics, University of Washington Bothell
18115 Campus Way NE, Bothell, WA 98011, United States


In this note, it is shown that if \ell and m are positive integers such that \ell > m, then there is a Perron number \rho such that \rho^n + (\rho + m)^n = (\rho + \ell)^n. It is also shown that there is an aperiodic integer matrix C such that C^n + (C+ m I_n)^n = (C + \ell I_n)^n.


  • Perron number
  • Fermat equation
  • Integer matrix
  • Aperiodic matrix

2020 Mathematics Subject Classification

  • 11D41
  • 15B36


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Cite this paper

Paparella, P. (2021). Perron numbers that satisfy Fermat’s equation. Notes on Number Theory and Discrete Mathematics, 27(3), 119-122, doi: 10.7546/nntdm.2021.27.3.119-122.

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