Proof of Fermat's Last Theorem (I Original)
Proof of Fermat's Last Theorem (I Original)
Proof of Fermat's Last Theorem
About natural number n more than 3,
The group (x, y, z) of the natural number
to become X^n + Y^n = Z^n does not exist.
◎In the case of an odd number (prime number)
Because the odd number all becomes the multiple of prime number,
Only in the case of a prime number, you should prove it.
Than a small theorem of Fermat
When I assume P a prime number,
α＾P － α ≡ ０ （mod P)
(But α and P mutually prime,
in other words,
assume P a prime number,
and do α with the integer that is not a multiple of P )
n at the time of prime number
n = P
X＾P ＋ Y＾P ＝ Z^P
I transform it and transform it like an expression below.
X＾P － X ＋ Y＾P － Y ＋ X ＋ Y ＝ Z＾P － Z ＋ Z
Than proof of Fermat's Last Theorem
P in the case of a prime number,
Because the thing of the form of α^P - α is divisible in P
It becomes the multiple of P
(But α and P mutually prime,
in other words,
assume P a prime number,
and do α with the integer that is not a multiple of P )
∴
X＾P - X ＝ PA , Y^P - Y = PB , Z^P - Z = PC
PA＋PB＋X＋Y ＝ PC ＋ Z
P（A＋B－C） ＝ Z -X -Y
A＋B－C ＝ Z/P -X/P -Y/P
Than proof of Fermat's Last Theorem
X≠P,Y≠P,Z≠ｐ, Neither X nor Y nor Z is multiples of P.
（Because A, B, C are natural number.
In the one which natural number does not have when I cannot divide Z,-X,-Y by P.
A numerical formula does not hold good)
∴
About natural number n more than 3,
The group (x, y, z) of the natural number
to become x^n + y^n = z^n does not exist.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
◎ In the case of (αP)^P
In the case of (αP)^P,
The small theorem of Fermat does not apply to it
So,
It is necessary to prove it in the case of (αP)^P.
X,Y,Z in the case of all, a multiple of P
X＝aP,Y=bP,Z=cP
(aP)^P + (bP)^P = (cP)^P
(a^P)(P^P) + (b^P)(P^P) = (c^P)(P^P)
a^P + b^P = c^P
∴
When a small theorem of Fermat applies to it, it is the same
(But α and P mutually prime,
in other words,
assume P a prime number,
and do α with the integer that is not a multiple of P )
among X,Y,Z,
When even one is P, but there is the thing which is not a multiple of P.
x^n + y^n = z^n does not hold good
(Like the case that a small theorem of Fermat applies to
than a small theorem of Fermat,
Because the thing which Not divisible by P comes out.)
∴
In the case of (αP)^P
About natural number n more than 3,
The group (x, y, z) of the natural number
to become x^n + y^n = z^n does not exist.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
◎n in the case of an even number
Fermat does proof at the age of n=4
∴
n in the case of an even number
About natural number n more than 3,
The group (x, y, z) of the natural number
to become x^n + y^n = z^n does not exist.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
∴
In the case of an even number
In the case of an odd number,
Both
About natural number n more than 3,
The group (x, y, z) of the natural number
to become x^n + y^n = z^n does not exist.
© June 2017 kanael(Nickname)
日本語（japanese)
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