District Rascani
Village Recea
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
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
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) :
If (1) is divided by cn it becomes:
can be definited as:
a) =d/10k, where d,k N
b) =t/10k*(10m-1), where t,m,k
Therefore (1) becomes
an+bn=10kn (6)
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 - does not has
solutions for n>2
an+bn=5n - does not has
solutions for n>2
Let now solve
where n>2 a,b,k,m,nN
Accordingly with theorem 1 (7) has solutions only if
an+bn=10mn or
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,
Sergiu Iaюco