You are wasting my time (and that of others.)
You claim Galois' duel was over Fermat's theorem, then provide a link that tells us what I already told you.
WTF are you doing?
I'll keep you off my ever-growing ignore list if you can make any sense of what you've said.
If you think that, then you know very little about this theorem.
As I clearly stated, Fermat actually wrote - by hand - that he had found a "remarkable proof" of the theorem but couldn't fit it into the margin he put the note in.
Just because it was never published (or found) doesn't mean he...
Fermat's last theorem - which is what you are talking about - isn't about cubes or cube roots. It states that there are no nonzero whole number solutions to this equation where n>2:
Fermat claimed that he had found a "remarkable proof" of this theorem in some notes he hand-wrote in the margin...