# On the Rational Solutions of $x^y = y^x$

by Marta Sved (The University of Adelaide Australia)

This article originally appeared in:
Mathematics Magazine
February, 1990

Subject classification(s): Calculus | Exponents | Arithmetic | Rational Numbers | Number Concepts | Numbers and Computation
Applicable Course(s): 4.3 Number Theory | 3.2 Mainstream Calculus II

The author provides a new way of finding all rational solutions of $x^y = y^x$ as well as a historical survey of this problem.

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Capsule Course Topic(s):
Number Theory | Diophantine Problems