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#### conscipost

##### Member

- Jan 26, 2012

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I was wondering if there is any way to know in general how many real solutions $x^n=n^x$ may have with n being a positive integer. Thanks!

Using IVT one can see that if n is even there must be at least three solutions, and if n is odd there exists at least two. But are these the "sharpest" bounds?

Using IVT one can see that if n is even there must be at least three solutions, and if n is odd there exists at least two. But are these the "sharpest" bounds?

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