Find all integers $x$ and $y$ such as that $ ^yx \ =\ ^xy$, where $^yx$ is a tetration.
Can it also be solved in real numbers?
I already know this: https://en.wikipedia.org/wiki/Tetration.
I tried experimenting a little, as well as trying to solve it, but I soon found out that it's out of my scope. I am asking for a solution here because I am highly interested in it and I haven't seen a post about it.