Numbers that commute under exponentiation in complex plane

• Mateja Grašič ^[1] ; Dušan Pagon ^[2]
  1. [1] Faculty of natural sciences and mhematics (Maribor, Eslovenia)
  2. [2] Inštitut za Matematiko, Fiziko in Mehaniko (Ljubljana, Eslovenia)
• Localización: Materials matemàtics, ISSN-e 1887-1097, Nº. 0, 2025
• Idioma: inglés
• Enlaces
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• Resumen

  • The raising to the a-th power and the exponential function with base a are defined for all positive arguments x, if a is any positive real number. For various a we calculate the coordinates of the non-trivial common point of the graphs of the above mentioned functions. We also discuss a similar problem for complex numbers defining a power dual number and show that there exist infinitely many numbers commuting with a given one under the exponentiation operation.

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