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PIERRE DE FERMAT' S LAST THEOREM.
CASE SPECIAL N=3 .
THE CONDITIONS.Z,X,Y,N ARE THE INTEGERS . Z*X*Y*N>0.N>2.
Z^3=/=X^3+Y^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.
Happy&Peace.
Trantancuong.
The equation a^n+b^n=c^n, n>2 , where n is a positive integer , has no non trivial integer solution (a,b,c).
First by Andrew Wiles-Very difficult proof
Now simple proofs are available;A simple and short analytical proof of Fermat's last theorem, CNMSEM,Vol.2,No.3 March 2011 pg.57-63
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What is the contribution of andrew wiles to mathematics?
He proved Fermat's Last Theorem. Actually he proved the Taniyama-Shimura-Weil conjecture and this proved the theorem.
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.
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.
What is a Theorem ender?
QED, Fermat's Last Theorem.
What Great Mathematicians are still alive?
Andrew Wiley, who solved Fermat's Last Theorem. Andrew Wiley, who solved Fermat's Last 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.
Fermat's Last Theorem was invented by who in 1847?
It was 1647 not 1847 and by Fermat himself.
What year was Fermat's last theorem?
1637
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.
What did Andrew wiles do?
He proved Fermat's last "theorem" which had been an open question for centuries and was one of the most famous open problems in all of mathematics.
What is the basic of Fermat's last Theorem?
The basis for Fermat's Last Theorem was Pythagoras's theorem. The latter showed that in any right angled triangle, the lengths of the sides satisfies a^2 + b^2 = c^2. In particular, that there are integer solutions to the equation: such as {3, 4, 5} or {5, 12, 13}. Fermat's theorem proved that there were no non-trivial solutions for a^n + b^n = c^n for any positive integers a, b, c and n where n > 2
True or false a theroem is a statement that can be easily proved?
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
