Iatco Sergiu. Simplification of prove of Fermat theorem

Iatco Sergiu. Simplification of prove of Fermat theorem



      R.Moldova
      District Rascani
      Village Recea
      itsergiu@yahoo.com
      Date: 4 May 1999

      Dear Sir,

      I am an amateur mathematician. First time I read about Fermat's last theorem when I was 15 years old. Just like other people from the beginning I dreamt to prove one day it. Last year I found out that A.Wiles and R.Taylor proved it. I read this proof and I found it (just like other people) too complex. I analysed the Fermat's last theorem and I succeed to simplify it as follows:

      Let have Fermat's equation:
      an+bn=cn , where n>2 (1)
      Because c=p1*...*pt, where pi - prime number, equation (1) becomes:
      an+bn= p1n*...*ptn (2)
      If exist such pi for which a1n+b1n= pin (3) has solutions then these solutions are also solutions for (2)
      Let r= p1*...*pi-1*pi+1*...*pt
      Multiplying (3) with rn we have:
      (r*a1)n+(r*b1)n= pin, let a=r*a1 b=r*b1
      an+bn= p1n*...*ptn - what had to be proved
      What must be proved but I could not is that (2) has solutions only if (3) has solutions
      Theorem 1 (unproved by me)
      an+bn= p1n*...*ptn - has sloutions only if a1n+b1n=pin
     
Let return to Fermat's equation (1) :
      an+bn=cn
     
If (1) is divided by cn it becomes:
      (*a)n+(*b)n=1
      can be definited as:
      a) =d/10k, where d,k N
      b) =t/10k*(10m-1), where t,m,k N
      Therefore (1) becomes
      (a*d)n+(b*d)n=(10k)n (4)
      (a*t)n+(b*t)n=10mn*(10k-1)n (5)
      or,
      an+bn=10kn (6)
      an+bn=10mn*(10k-1)n (7)
      Therefore in order to prove (1) must be proved that (6) and (7) do not have solutions for n>2.
      Let solve first an+bn=10kn
     
Accordingly with theorem 1 (6) has solution only if
      an+bn=5n or an+bn=2n
      an+bn=2n - does not has solutions for n>2
      an+bn=5n - does not has solutions for n>2
      Let now solve an+bn=10mn*(10k-1)n, where n>2 a,b,k,m,nN
      Accordingly with theorem 1 (7) has solutions only if
      an+bn=10mn or an+bn=(10k-1)n
     
an+bn=10mn has already been examined
      Therefore must be proved:
      an+bn=(10k-1)n (8)
      Regretfully I could not prove (8).
      Finally in order to prove Fermat's theorem must be proved theorem 1 and equation (8).
      I will be happy if you publish my work and after that somebody will come with a simply proof like Fermat's ones.
      Of course you should publish it only if I am not wrong.
      I will be grateful if you give me an answer to my letter.

      Thank you,
      Respectfully,
      Sergiu Iaco


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