Articles
Two centuries of the equations of commutativity and associativity of exponentiation
Published:
2003-12-01
https://doi.org/10.5485/TMCS.2003.0022
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Keywords
commutativity of exponentiation associativity of exponentiation parametrizations of the solution set
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Copyright (c) 2003 Lajos Lóczi
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Lóczi, L. (2003). Two centuries of the equations of commutativity and associativity of exponentiation. Teaching Mathematics and Computer Science, 1(2), 219-233. https://doi.org/10.5485/TMCS.2003.0022
Abstract
In this survey article we guide the reader through the solution of the commutative equation of exponentiation x^y = y^x and that of the associative equation of exponentiation x^(y^z) = (x^y)^z. Various characterizations of the integer, rational, real and complex solutions are discussed together with some new results and open directions. The article is supplemented by a detailed and commented bibliography on the history of these equations.