## 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:
a^{n}+b^{n}=c^{n} , where n>2 (1)
Because c=p1*...*pt, where pi - prime number, equation (1) becomes:
a^{n}+b^{n}= p1^{n}*...*pt^{n}
(2)
If exist such pi for which a1^{n}+b1^{n}=
pi^{n} (3) has solutions then these solutions are also solutions
for (2)
Let r= p1*...*pi-1*pi+1*...*pt
Multiplying (3) with r^{n }we have:
(r*a1)^{n}+(r*b1)^{n}= pi^{n}, let a=r*a1
b=r*b1
a^{n}+b^{n}= p1^{n}*...*pt^{n}
- 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)
a**^{n}+b^{n}= p1^{n}*...*pt^{n}
- has sloutions only if a1^{n}+b1^{n}=pi^{n
}Let return to Fermat's equation (1) :
a^{n}+b^{n}=c^{n
}If (1) is divided by c^{n} it becomes:
(*a)^{n+}(*b)^{n}=1
can be definited as:
a) =d/10^{k}, where ^{ }d,k N
b) =t/10^{k}*(10^{m}-1), where ^{ }t,m,k
N
Therefore (1) becomes
(a*d)^{n}+(b*d)^{n}=(10^{k})^{n
} (4)
(a*t)^{n}+(b*t)^{n}=10^{mn}*(10^{k}-1)^{n}
(5)
or,
a^{n}+b^{n}=10^{kn } (6)
a^{n}+b^{n}=10^{mn}*(10^{k}-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 a^{n}+b^{n}=10^{kn
}Accordingly with **theorem 1** (6) has solution only if
a^{n}+b^{n}=5^{n} or
a^{n}+b^{n}=2^{n}
a^{n}+b^{n}=2^{n} - does not has
solutions for n>2
a^{n}+b^{n}=5^{n} - does not has
solutions for n>2
Let now solve
a^{n}+b^{n}=10^{mn}*(10^{k}-1)^{n},
where n>2 a,b,k,m,nN
Accordingly with **theorem 1** (7) has solutions only if
a^{n}+b^{n}=10^{mn} or
a^{n}+b^{n}=(10^{k}-1)^{n
}a^{n}+b^{n}=10^{mn} has already
been examined
Therefore must be proved:
a^{n}+b^{n}=(10^{k}-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 IaÀco*

ðÏÐÕÌÑÒÎÏÓÔØ: **19**, Last-modified: Tue, 04 May 1999 14:27:15 GMT