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Pierre de Fermat's laatste stelling
(x, y, z, n) element van de (N +) ^ 4
n> 2
(a) element van de Z
F is de functie (s).
F (a) = [a (a +1) / 2] ^ 2
F (0) = 0 en F (-1) = 0
Beschouw twee vergelijkingen.
F (z) = F (x) + F (y)
F (z-1) = F (x-1) + F (y-1)
We hebben een keten van gevolgtrekking
F (z) = F (x) + F (y) gelijkwaardig F (z-1) = F (x-1) + F (y-1)
F (z) = F (x) + F (y) conclusie F (z-1) = F (x-1) + F (y-1)
F (z-x-1) = F (x-x-1) + F (y-x-1) conclusie F (z-x-2) = F (x-x-2) + F (y-x-2)
zien we
F (z-x-1) = F (x-x-1) + F (y-x-1)
F (z-x-1) = F (-1) + F (y-x-1)
F (z-x-1) = 0 + F (y-x-1)
conclusie
z = y
en
F (z-x-2) = F (x-x-2) + F (y-x-2)
F (z-x-2) = F (-2) + F (y-x-2)
F (z-x-2) = 1 + F (y-x-2)
conclusie
z = / = y.
conclusie
F (z-x-1) = F (x-x-1) + F (y-x-1) geen conclusie (z-x-2) = F (x-x 2) + F (y-x-2)
conclusie
F (z) = F (x) + F (y) geen conclusie F (z-1) = F (x-1) + F (y-1)
conclusie
F (z) = F (x) + F (y) zijn niet equivalent van F (z-1) = F (x-1) + F (y-1)
Daarom is de twee gevallen.
[F (x) + F (y)] = F (z) en F (x-1) + F (y-1)] = / = F (Z-1)
of vice versa
conclusie
[F (x) + F (y)] - [F (x-1) + F (y-1)] = / = F (z) - F (z-1).
of
F (x) - F (x-1) + F (y)-F (y-1) = / = F (z) - F (z-1).
zien we
F (x) - F (x-1) = [x (x 1) / 2] ^ 2 - [(x-1) x / 2] ^ 2
= (X ^ 4 +2 x ^ 3 + x ^ 2/4) - (x ^ 4-2x 3 + x ^ ^ 2/4).
= X ^ 3
F (y)-F (y-1) = y ^ 3
F (z)-F (z-1) = z ^ 3
conclusie
x 3 + y ^ 3 = / = z ^ 3
n> 2. lossen soortgelijke
We hebben een keten van gevolgtrekking
G (z) * F (z) = G (x) * F (x) + G (y) * F (y) gelijkwaardig G (z) * F (z-1) = G (x) * F ( x -1) + G (y) * F (y-1)
G (z) * F (z) = G (x) * F (x) + G (y) * F (y) conclusie G (z) * F (z-1) = G (x) * F (x -1) + G (y) * F (y-1)
G (z) * F (z-x-1) = G (x) * F (x-x-1) + G (y-x-1) * F (y) conclusie G (z) * F (z-x-2) = G ( x) * F (x-x 2) + G (y) * F (y-x 2)
zien we
G (z) * F (z-x-1) = G (x) * F (x-x-1) + G (y) * F (y-x-1)
G (z) * F (z-x-1) = G (x) * F (-1) + G (y) * F (y-x-1)
G (z) * F (z-x-1) = 0 + G (y) * F (y-x-1)
conclusie
z = y.
en
G (z) * F (z-x-2) = G (x) * F (x-x-2) + G (y) * F (y-x-2)
G (z) * F (z-x-2) = G (x) * F (-2) + G (y) * F (y-x-2)
G (z) * F (z-x-2) = G (x) + G (y) * F (x-y-2)
x> 0 conclusie G (x)> 0
conclusie
z = / = y.
conclusie
G (z) * F (z-x-1) = G (x) * F (x-x-1) + G (y-x-1) * F (y) geen conclusie G (z) * F (z-x-2) = G (x) * F (x-x-2) + G (y) * F (y-x-2)
conclusie
G (z) * F (z) = G (x) * F (x) + G (y) * F (y) geen conclusie G (z) * F (z-1) = G (x) * F ( x-1) + G (y) * F (y-1)
conclusie
G (z) * F (z) = G (x) * F (x) + G (y) * F (y) zijn niet equivalent van G (z) * F (z-1) = G (x) * F (x-1) + G (y) * F (y-1)
Daarom is de twee gevallen.
[G (x) * F (x) + G (y) * F (y)] = G (z) * F (z) en [G (x) * F (x-1) + G (y) * F (y-1)] = / = G (z-1) * F (z-1)
of vice versa
conclusie
[G (x) * F (x) + G (y) * F (y)] - [G (x) * F (x-1) + G (y) * F (y-1)] = / = G (z) * [F (z) -F(Z-1)].
of
G (x) * [F (x) - F (x-1)] + G (y) * [F (y) - F (y-1)] = / = G (z) * [F (z) - F(z-1)]
zien we
x ^ n = G (x) * [F (x) - F (x-1)]
y ^ n = G (y) * [F (y) - F (y-1)]
z ^ n = G (z) * [F (z) - F (z-1)]
conclusie
x ^ n + y ^ n = / = z ^ n
gelukkig en vrede
Tran tan Cuong .
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∙ 11y ago
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Who was able to solve Fermat's theorem in 1994?
Andrew Wiles
The most hardest equation to solve?
Fermat's Last Theorem
How long did it take to solve Fermat's last theorem?
long time.
Which mathmatician is most famous for claiming that he solved a problem which took many mathematicians over 300 years after his death to solve?
Pierre de Fermat. The problem was called Fermat's Last Theorem
When was Fermat Prize created?
Fermat Prize was created in 1989.
Is anything named after Pierre de Fermat?
Yes, the famous Fermat's Last Theorem, a conjecture by Fermat, that an equation of the form an + bn = cn has no integer solution, for n > 2. This was conjectured by Fermat in 1637, but it was only proved in 1995.Yes, the famous Fermat's Last Theorem, a conjecture by Fermat, that an equation of the form an + bn = cn has no integer solution, for n > 2. This was conjectured by Fermat in 1637, but it was only proved in 1995.Yes, the famous Fermat's Last Theorem, a conjecture by Fermat, that an equation of the form an + bn = cn has no integer solution, for n > 2. This was conjectured by Fermat in 1637, but it was only proved in 1995.Yes, the famous Fermat's Last Theorem, a conjecture by Fermat, that an equation of the form an + bn = cn has no integer solution, for n > 2. This was conjectured by Fermat in 1637, but it was only proved in 1995.
What was Pierre De Fermat family history?
who meny juseph have fermat
When was Fermat's Room created?
Fermat's Room was created on 2007-10-07.
Fermat's Last Theorem was invented by who in 1847?
It was 1647 not 1847 and by Fermat himself.
What is Pierre de fermat famous for?
Pierre De Fermat is famous for Fermat's Last Theorem, which states that an+bn=cn will never be true as long as n>2
What is a Fermat prime?
A Fermat Prime refers to a proof that the mathematician Fermat discovered. It refers to a integer that is subject to an equation and the predictable result. Below is a webpage that explains it with examples.
When was Pierre de Fermat born?
Pierre de Fermat was born on August 17, 1601.
