Perron numbers that satisfy Fermat’s equation
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Published:2021-09
Issue:3
Volume:27
Page:119-122
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ISSN:1310-5132
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Container-title:Notes on Number Theory and Discrete Mathematics
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language:
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Short-container-title:NNTDM
Author:
Paparella Pietro,
Abstract
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.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)