On the odd prime solutions of the Diophantine equation \(x^y + y^x = z^z\). (English) Zbl 1470.11053
Summary: Using the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation \(x^y + y^x = z^z\) has no positive integer solutions (\(x, y, z\)) with \(x\) and \(y\) being odd primes.
MSC:
| 11D61 | Exponential Diophantine equations |
References:
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