What is a Possible Algebraic Proof of Case 1 of Fermat's Last Theorem?

[vantheman]

Most with any knowledge of Number Theory are aware that many hundreds of thousands of hours have been spent reviewing flawed "proofs" of Fermat's Last Theorem (FLT). It is understandable that a serious mathematician would not spend more than a few minutes looking at a possible "proof". Wiles' proof is magnificient, if you have a strong background in higher mathematics, which very few do. The link below is a 'possible' algebraic proof of Case 1 that, if it doesn't have a fatal flaw, may be a solution that a math undergraduate can understand. I hope you will not find it a waste of time to take a look.

http://dutch-fltcase1.blogspot.com/

 

[dodo]

Hi, vantheman,
I have a couple of questions:

1) Case 1 says "n divides neither of x,y,z"; yet for Section I, at the beginning of page 9, you take the condition (n,x) = (n,y) = (n,z) = 1, which is much stronger. (For example, 6 does not divide any of 8, 11, 17, yet it has a common factor with the first of them.)

2) Also on page 9, eq.1.6, I believe you are trying to find a factor h in the right-hand side, and all terms have one h except the last, a^n . n^(n-2). Why can't the factor h be in n^(n-2)? Or, for that matter, h could be composite, with some of its prime factors in a^n and the others in n^(n-2).

Thanks

 

[vantheman]

I am assuming the stronger position - n does not divide x, y or z and x, y and z have no common factors.

Since n does not divide y , n does not divide h, since y == h mod n. Therefore h cannot have any n factors.