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

: 34, Last-modified: Tue, 04 May 1999 14:27:15 GMT