We are supposed to find all whole numbers n > 2, such that:
$$ \exists x \in \mathbb{N}: n^{n-2} = x^{n} $$
We can modify the expression to:
$$ x = n^{\frac{n-2}{n}} $$
Or perhaps even:
$$ x = \frac{n}{n^{2/n}} $$
Intuitively it makes sense to me that the only number that makes sense as an answer is 4. How would I go about proving that x is not a whole number for all other n?