Freudenthal started his career as an assistant to Brouwer, so I am not surprised Intuitionism was often on his mind, with or without the incompleteness theorem.

I guess quid meant $n>2$; there are surely infinitely many solutions to $x+1=y^q$...

I found the thesis (a hard copy, no digital version available) in the catalogue of the library of the University of Amsterdam (permalink.opc.uva.nl/item/002887553). I won't be in town for the coming week, but if you haven't found another version by then it would be no problem to send you a scan.

Paul: The linked article seems to be about the \emph{possibility} of a smooth choice of a root of what is here called $f^2$. In your example, $|x|$ is a bad choice, $x$ is a good one.

I just realized you probaby write a version of the Cyrillic alphabet, so you will need 31 or even 34 kids. Excuse my latinocentrism!