Summary of the AP proofs of Beal and then FLT #1474 Correcting Math
I spent the day being vexed by FLT then Beal, in that order. How so easy it is to prove FLT once Beal is proved. Yet the other way around, trying to prove FLT without the use of Beal is so much worse. Without using Beal results, FLT becomes loaded with cases. With Beal results, all the cases vanish.
Maybe I am just being lazy and wanting to get out of numerous cases. Or, maybe the Beal is not really a generalization but rather a ancillary offshoot, a related conjecture but different and not having FLT as a corollary. I am trying to think of other proofs with a strange relationship of general to corollary.
So the vexation is, how can a more general theorem be easier to prove than a less general?
I may have to backtrack, retrench. And do the Beal proof first and then use it to prove FLT, although it is automatic.
I am trying to figure out the logic of this, of why the more general has a fast and easy proof, yet the minor problem of FLT is almost impervious of a proof unless you use the Beal portions.
I am stumped and baffled and cannot think of any other example in mathematics where the general has to be proven before the specific case. I need the fact of a prime divisor for A,B,C in order to prove FLT. So that if we have 2^3 +4^3 the C must be 8^3. And if we have 3^3 + 6^3, then the C must be 9^3, yet those are impossible.
So I need to ponder on this some more, and unless I can resolve it, I must revert back to the original plan of Beal first then using Beal to prove FLT.
Now that would be interesting if it is true, because then since Wiles's methods cannot do Beal at all, means his FLT is flawed and nonrepairable.
I cannot think of any other theorem in math that required the proof of the general case and then go back and able to prove the minor specific case. If true, then I doubt Beal and FLT are the first and only ones.
Recently I re-opened the old newsgroup of 1990s and there one can read my recent posts without the hassle of mockers and hatemongers.