In article <email@example.com>, firstname.lastname@example.org wrote: > In article <email@example.com>, > firstname.lastname@example.org wrote: > > In article <email@example.com>, > > firstname.lastname@example.org wrote: > > > You say, I'm forced to act like I'm outside of integers at the > start, > > > but what if there were an integer solution to FLT? > > > > > > Then wouldn't your objection fall away? > > > > No. > > > > One proof of Fermat's result that primes congruent to 1 modulo 4 > > can be written as the sum of the squares of two integers uses > > complex numbers (in particular, Gaussian integers). You are > > proving a result about integers, there are integer solutions for > > the result, yet you go outside to complex numbers (and you have > > to specify that you are going out to complex numbers so that > > you can use their properties). > > > > Nope. Turns out that it depends on what I call 'v' in the proof.
I think you misunderstood what I meant by "One proof of Fermat's result that ...". I am not referring to Fermat's last theorem or to your proof of Fermat's last theorem.
I am referring to the result of Fermat that says 5 = 1^2 + 2^2, 13 = 2^2 + 3^2, 17 = 1^2 + 4^2, 29 = 2^2 + 5^2, etc but the primes 3, 7, 11, 19, 23, etc cannot be expressed as a sum of two squares.