I think all this means is that you find this proof less obvious than some other proofs. That’s fair enough, but finding something difficult to grasp doesn’t mean it’s likely to be wrong.
The way it looks to me: no, it’s not feasible, it’s plainly not feasible, for exactly the reason cousin_it gives; you might as well be asking for three positive integers with x^3+y^3=z^3. (Actually, even more so; I find the cardinality argument here clear at a glance, but Euler’s infinite-descent argument intricate and requiring sustained concentration. But, again, the fact that I can’t just look at it and immediately see why there are no solutions in no way calls into question the proof that there are no solutions.)
I think all this means is that you find this proof less obvious than some other proofs. That’s fair enough, but finding something difficult to grasp doesn’t mean it’s likely to be wrong.
The way it looks to me: no, it’s not feasible, it’s plainly not feasible, for exactly the reason cousin_it gives; you might as well be asking for three positive integers with x^3+y^3=z^3. (Actually, even more so; I find the cardinality argument here clear at a glance, but Euler’s infinite-descent argument intricate and requiring sustained concentration. But, again, the fact that I can’t just look at it and immediately see why there are no solutions in no way calls into question the proof that there are no solutions.)