```óĎÄĹŇÖÁÎÉĹFine HTMLPrinted versiontxt(Word,ëđë)Lib.ru htmlIatco 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
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
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 IaŔco
đĎĐŐĚŃŇÎĎÓÔŘ: 19, Last-modified: Tue, 04 May 1999 14:27:15 GMT

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