Hello,

Substitute and in and prove it is equal to n if .

This proves that if is solution, then is solution too.

If there is no solution, we're done.

If there is one solution, , and therefore is solution too. Since , we can prove the same way as above that is solution too. And so on...

Isn't it the infinite ascent ?

So either there is no solution, either there's an infinity of solutions.