FLT For Fun

Hi Tony, I think your claim should be considered as a corallary. That is an obvious result after a proof or lemma has been proven. It is clear that if a, b, and c are real numbers, then there will a solution. Thus no proof is required. Irrational number is a subset of real number. It's the integer part that made FLT difficult to prove. Many amateur and seasoned mathematicians approached FLT as a^n+b^n-c^n=0. That leads to solve equation of 3 unknowns. Direct approch proof would be impossible. Thus the indirect proofs have been devised. For example, elliptic curve (I called it fancy geometry). I know very little about it. But it is a big thing for math gurus. Cheers, flt4fun

I am new to this forum and I am not mathematician. I believe that Diophantus dealt with integers only. Furthermore you can't prove conjecture with another conjecture. I tried to prove FLT as a brain excercise a la Sudoku. Here what I can share. A proof using Euclidian geometry won't work. As for proving algebraically, it can be round robin. It will make you lost and give you a false sense of victory, and only few days later you will find yourselve back to square one. FLT is as false as 2=1. Finally if your proof is more than a page then it's no longer that elementary. flt4fun

Hi Robert, Your statement " (c^n + b^n) equals 2b^n + a^n and that shure is coprime to a, since a and b are coprimes." needs to be proved that they are coprime. Your approach is very interesting but your current form of proof would never pass the eyes of mathematicians. I tried to prove FLT on the side as brain exercise, a la, Sudoku. But I'd also like to see how other doing their proofs. I believe that I have a proof. Let me summarize what I know about FLT. FLT looks so innocent but it is as false statement as 2=1. If you want to prove it via geometry, then no Euclidian geometry will not prove it. The only geometry used to prove FLT is elliptic curve. The proof was over hundred pages long. Since I am not a mathematician but I am sure it is non-Euclidian geometry. As for algebraic proof, it can be round robin. But if you can stop it you prove it. flt4fun