
Fermat's last theorem
Posted:
Oct 20, 2017 7:33 AM


Hey guys, i'm new here and i would like to get some input about a possible proof of fermat's last theorem. I do think i didnt make any mistakes, but i would like to see wether i actually did. Here is it:
We have A^n+B^n = C^n (1)
We state that B<A<C<A+B, (2) gcd(a,b) = gcd(a,c) = gcd(b,c) = 1 All numbers are part of N
And we assume that n is odd and bigger than 2 C = (P^k)*D with P prime
We rewrite (1) as
(E)^n + (F)^n = P^(kn)
Where E and F are A/D and B/D respectively We can rewrite the left side as
(E+F)* (E^(n1)E^(n2)*F +... E*F^(n2)+F^(n1))
We know from (2) that P^k<E+F< 2*P^k
This also means however that the other part, which we replace as S, holds true to these conditions: P^(knk)÷2 < S < P^(knk)
These inequalities mean that (E+F) can be a multiple of P^(k1) at most, while S can be a multiple of P^(nkk1) at most.
This means however that the product of those two parts can only be a pruduct of P^(nk2) at most, since P is prime. We see a clear contradiction, so we conclude that there doesnt exist an odd number n where the equation is true.
This coupled with the proof of fermat himself for n=4, proves that there does not exist any n bigger than 2 where the equation is true

