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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 Iaюco

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