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PIERRE DE FERMAT' S LAST THEOREM.
CASE SPECIAL N=3 AND.GENERAL CASE N>2. .
THE CONDITIONS.Z,X,Y,N ARE THE INTEGERS . Z*X*Y*N>0.N>2.
Z^3=/=X^3+Y^3 AND Z^N=/=X^N+Y^N.
SPECIAL CASE N=3.
WE HAVE
(X^2+Y^2)^2=X^4+Y^4+2X^2*Y^2.
BECAUSE
X*Y>0=>2X^2*Y^2>0.
SO
(X^2+Y^2)^2=/=X^4+Y^4.
CASE 1. IF
Z^2=X^2+Y^2
SO
(Z^2)^2=(X^2+Y^2)^2
BECAUSE
(X^+Y^2)^2=/=X^4+Y^4.
SO
(Z^2)^2=/=X^4+Y^4.
SO
Z^4=/=X^4+Y^4.
CASE 2. IF
Z^4=X^4+Y^4
BECAUSE
X^4+Y^4.=/= (X^2+Y^2.)^2
SO
Z^4=/=(X^2+Y^2.)^2
SO
(Z^2)^2=/=(X^2+Y^2.)^2
SO
Z^2=/=X^2+Y^2.
(1) AND (2)=> Z^4+Z^2=/=X^4+Y^4+X^2+Y^2.
SO
2Z^4+2Z^2=/=2X^4+2Y^4+2X^2+Y^2.
SO
(Z^4+Z^2+2Z^3+Z^4+Z^2-2Z^3)=/=(X^4+X^2+2X^3+X^4+X^2-2X^3)+)(Y^4+Y^2+2Y^3+Y^4+Y^2-2Y^3)
SO IF
(Z^4+Z^2+2Z^3)/4=(Z^4+Z^2+2Z^3)/4+(Z^4+Z^2+2Z^3)/4
=> (Z^4+Z^2-2Z^3)/4=/=(Z^4+Z^2-2Z^3)/4+(Z^4+Z^2-2Z^3/4)
AND
SO IF
(Z^4+Z^2-2Z^3)/4=(Z^4+Z^2-2Z^3)/4+(Z^4+Z^2-2Z^3)./4
=> (Z^4+Z^2+2Z^3)/4=/=(Z^4+Z^2+2Z^3)/4+(Z^4+Z^2+2Z^3)/4
BECAUSE
(Z^4+Z^2+2Z^3)/4 - (Z^4+Z^2-2Z^3)/4 =Z^3.
SO
Z^3=/=X^3+Y^3.
GENERAL CASE N>2.
Z^N=/=X^N+Y^N.
WE HAVE
[X^(N-1)/2+Y^(N-1)/2]^(N+1)/(N-1)=X^(N+1)/2+Y^(N+1)/2+ H.
BECAUSE X*Y>0=>H>0.
SO
[X^(N-1)/2+Y^(N-1)/2]^(N+1)/(N-1)=/= X^(N+1)/2+Y^(N+1)/2
CASE 1. IF
Z^(N-1)/2=X^(N-1)/2+Y^(N-1)/2
SO
[Z^(N-1)/2]^(N+1)/(N-1)=[X^(N-1)/2+Y^(N-1)/2 ]^(N+1)/(N-1).
BECAUSE
[X^(N-1)/2+Y^(N-1)/2 ]^(N+1)/(N-1)=/=X^(N+1)/2+Y(N+1)/2.
SO
[Z^(N-1)/2]^(N+1)/(N-1)=/=X^(N+1)/2+Y(N+1)/2.
SO
Z^(N+1)/2=/=X^(N+1)/2+Y^(N+1)/2.
CASE 2. IF
Z^(N+1)/2=X^(N+1)/2+Y^(N+1)/2
SO
[Z^(N+1)/2]^(N-1)/(N+1)=[X^(N+1)/2+Y^(N+1)/2 ]^(N-1)/(N+1)
BECAUSE
[X^(N+1)/2+Y^(N+1)/2](N-1)/(N+1)=/=X(N-1)/2+Y^(N-1)/2.
SO
[Z^(N+1)/2]^(N-1)/(N+1)=/=X(N-1)/2+Y^(N-1)/2.
SO
Z^(N-1)/2=/=X(N-1)/2+Y^(N-1)/2..
SO
(1) AND (2)=> Z^(N+1)/2+Z^(N-1)/2=/=X^(N+1)/2+Y^(N+1)/2+X^(N-1)/2+Y^(N-1)/2.
SO
2[Z^(N+1)/2+Z^(N-1)/2]=/=2[X^(N+1)/2+Y^(N+1)/2]+2[X^(N-1)/2+Y^(N-1)/2.]
SO
[Z^(N+1)/2+Z^(N-1)/2+2Z^N ]+[Z^(N+1)/2+Z^(N-1)/2-2Z^N ]=/=[X^(N+1)/2+X^(N-1)/2+2X^N ]+[X^(N+1)/2+X^(N-1)/2-2X^N ]+[Y^(N+1)/2+Y^(N-1)/2+2Y^N ]+[Y^(N+1)/2+Y^(N-1)/2-2Y^N ]
SO IF
[Z^(N+1)/2+Z^(N-1)/2+2Z^N ]/4=[X^(N+1)/2+X^(N-1)/2+2X^N ] /4+ [Y^(N+1)/2+Y^(N-1)/2+2Y^N ]/4=>
[Z^(N+1)/2+Z^(N-1)/2-2Z^N ]/4=/=[X^(N+1)/2+X^(N-1)/2-2X^N ] /4+ [Y^(N+1)/2+Y^(N-1)/2-2Y^N ]/4
AND
IF
[Z^(N+1)/2+Z^(N-1)/2-2Z^N ]/4=[X^(N+1)/2+X^(N-1)/2-2X^N ] /4+ [Y^(N+1)/2+Y^(N-1)/2-2Y^N ]/4
=>
[Z^(N+1)/2+Z^(N-1)/2+2Z^N ]/4=/=[X^(N+1)/2+X^(N-1)/2+2X^N ]/4 + [Y^(N+1)/2+Y^(N-1)/2+2Y^N ]/4
BECAUSE
[Z^(N+1)/2+Z^(N-1)/2+2Z^N ] /4- [Z^(N+1)/2+Z^(N-1)/2-2Z^N ]/4=Z^N.
SO
Z^N=/=X^N+Y^N
HAPPY&PEACE.
Trantancuong.
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Did anyone oppose to the pythgreom theorm?
Although the Pythagorean theorem (sums of square of a right angled triangle) is called a theorem it has many mathematical proofs (including the recent proof of Fermats last theorem which tangentially also prooves Pythagorean theorem). In fact Pythagorean theorem is an 'axiom', a kind of 'super law'. It doesn't matter if anyone does oppose it, it is one of the few fundamental truths of the universe.
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 number that no value of can be greater than for the solutions to the equation in fermats last theorem?
Fermat's last theorem states that the equation xn + yn = zn has no integer solutions for x, y and z when the integer n is greater than 2. When n=2, we obtain the Pythagoras theorem.
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 a Theorem ender?
QED, Fermat's Last Theorem.
Who is person who is solving Fermat?
Andrew Wiles solved/proved Fermats Last Theorem. The theorem states Xn + Yn = Zn , where n represents 3, 4, 5,......... there is no solution.
Did anyone oppose to the pythgreom theorm?
Although the Pythagorean theorem (sums of square of a right angled triangle) is called a theorem it has many mathematical proofs (including the recent proof of Fermats last theorem which tangentially also prooves Pythagorean theorem). In fact Pythagorean theorem is an 'axiom', a kind of 'super law'. It doesn't matter if anyone does oppose it, it is one of the few fundamental truths of the universe.
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 fermats last theorem?
Fermat's Last Theorem is sometimes called Fermat's conjecture. It states that no three positive integers can satisfy the equation a*n + b*n = c*n, for any integer n greater than two.
What is the number that no value of can be greater than for the solutions to the equation in fermats last theorem?
Fermat's last theorem states that the equation xn + yn = zn has no integer solutions for x, y and z when the integer n is greater than 2. When n=2, we obtain the Pythagoras theorem.
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.
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 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.
Was Fermat's Last Theorem really his last theorem?
This was not the last theorem that Fermat wrote. Rather, it was the last one to be proven/disproven.
How many pages does The Last Theorem have?
The Last Theorem has 311 pages.
When was The Last Theorem created?
The Last Theorem was created in 2008-07.
