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Pierre De Fermat 's last Theorem.
The conditions:
x,y,z,n are the integers and >0. n>2.
Proof:
z^n=/x^n+y^n.
We have;
z^3=[z(z+1)/2]^2-[(z-1)z/2]^2
Example;
5^3=[5(5+1)/2]^2-[5(5-1)/2]^2=225-100=125
And
z^3+(z-1)^3=[z(z+1)/2]^2-[(z-2)(z-1)/2]^2
Example;
5^3+4^3=[5(5+1)/2]^2-[(5-2)(5-1)/2]^2=225-36=189
And
z^3+(z-1)^3+(z-2)^3=[z(z+1)/2]^2-[(z-3)(z-2)/2]^2
Example
5^3+4^3+2^3=[5(5+1)/2]^2-[(5-3)(5-2)/2]^2=225-9=216
And
z^3+(z-1)^3+(z-2)^3+(z-3)^3=[z(z+1)/2]^2-[(z-4)(z-3)/2]^2
Example
5^3+4^3+3^3+2^3=[5(5+1)/2]^2-[(5-4)(5-3)/2]^2=225-1=224
General:
z^3+(z-1)^3+....+(z-m)^3=[z(z+1)/2]^2-[(z-m-1)(z-m)/2]^2
We have;
z^3=z^3+(z-m-1)^3 - (z-m-1)^3.
Because:
z^3+(z-m-1)^3=[z^3+(z-1)^3+....+(z-m-1)^3] - [(z-1)^3+....+(z-m)^3]
So
z^3=[z(z+1)/2]^2-[(z-m-2)(z-m-1)/2]^2 - [z(z-1)/2]^3+[(z-m-1)(z-m)/2]^2 - (z-m-1)^3.
Similar:
z^3=z^3+(z-m-2)^3 - (z-m-2)^3.
So
z^3=[z(z+1)/2]^2-[(z-m-3)(z-m-2)/2]^2 - [z(z-1)/2]^3+[(z-m-2)(z-m-1)/2]^2 - (z-m-2)^3.
....
....
Suppose:
z^n=x^n+y^n
So
z^(n-3)*z^3=x^(n-3)^n*x^3+y^(n-3)*y^3.
So
z^(n-3)*{[z(z+1)/2]^2-[(z-m-2)(z-m-1)/2]^2 - [z(z-1)/2]^3+[(z-m-1)(z-m)/2]^2 - (z-m-1)^3}=x^(n-3)*{[x(x+1)/2]^2-[(x-m-2)(x-m-1)/2]^2 - [x(x-1)/2]^3+[(x-m-1)(x-m)/2]^2 - (x-m-1)^3}+y^(n-3)*{[y(y+1)/2]^2-[(y-m-2)(y-m-1)/2]^2 - [y(y-1)/2]^3+[(y-m-1)(y-m)/2]^2 - (y-m-1)^3}
Similar:
z^(n-3)*{[z(z+1)/2]^2-[(z-m-3)(z-m-2)/2]^2 - [z(z-1)/2]^3+[(z-m-2)(z-m-1)/2]^2 - (z-m-2)^3=x^(n-3)*{[x(x+1)/2]^2-[(x-m-3)(x-m-2)/2]^2 - [x(x-1)/2]^3+[(x-m-2)(x-m-1)/2]^2 - (x-m-2)^3+y^(n-3)*{[y(y+1)/2]^2-[(y-m-3)(y-m-2)/2]^2 - [y(y-1)/2]^3+[(y-m-2)(y-m-1)/2]^2 - (y-m-2)^3.
....
....
Because it is codified .
So
Impossible all are the integers.
So:
z^n=/x^n+y^n.
ISHTAR.
Wiki User
∙ 11y ago
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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.
What was Fermat's original proof of his last theorem?
Fermat's last theorem says there does not exist three positive integers a, b, and c which can satisfy the equation an + bn = cn for any integer value of n greater than 2. (2 with be pythagoran triples so we don't include that) Fermat proved the case for n=4, but did not leave a general proof. The proof of this theorem came in 1995. Taylor and Wiles proved it but the math they used was not even known when Fermat was alive so he could not have done a similar proof.
What is the answer for Fermat's Last Theorem?
Fermat's Last Theorem states that an + bn = cn does not have non-zero integer solutions for n > 2. Various mathematicians have worked on Fermat's Last Theorem, proving it true for certain cases of n. In 1994, Andrew Wiles revised and corrected his 1993 proof of the theorem for all cases of n. The proof is very complex.
Where did Fermat write his last theorem?
He didn't write it. What he did was to write in the margin of a book that he had a proof but there was not enough space to write it there.
Why wasn't Fermats last theorem written on paper?
But it was. That is why we know about it. If you mean why the PROOF was not written- Fermat wrote that he had found a wonderful proof for the theorem, but unfortunately the margin was too small to contain it. This is why the theorem became so famous- being understandable by even a schoolchild, but at the same time so hard to prove that even the best mathematicians had to surrender, with a simple proof seemingly being existent that just nobody except Fermat could find. The theorem has since been proven but the proof uses math tools that are very advanced and were not available in Fermat's life-time.
What is the proof to Fermat's last theorem?
British mathematician Andrew Wiles published a proof of Fermat's Last Theorem in May of 1995, 358 years after the conjecture was first proposed. The proof itself is over 150 pages long and took him seven years to create. As you might imagine, it is not reproducible here, but it and a great many supporting articles are readily available online.
What is Fermat's Sandwich Theorem?
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Is All about math 5 pages?
I'd say thousands of pages. The proof of Fermat's last theorem (alone) was over 100 pages.
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
Fermat's Last Theorem was invented by who in 1847?
It was 1647 not 1847 and by Fermat himself.
