Best Answer

PIERRE DE FERMAT's last Theorem.

(x,y,z,n) belong ( N+ )^4..

n>2.

(a) belong Z

F is function of ( a.)

F(a)=[a(a+1)/2]^2

F(0)=0 and F(-1)=0.

Consider two equations

F(z)=F(x)+F(y)

F(z-1)=F(x-1)+F(y-1)

We have a string inference

F(z)=F(x)+F(y) equivalent F(z-1)=F(x-1)+F(y-1)

F(z)=F(x)+F(y) infer F(z-1)=F(x-1)+F(y-1)

F(z-x-1)=F(x-x-1)+F(y-x-1) infer F(z-x-2)=F(x-x-2)+F(y-x-2)

we see

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 )

give

z=y

and

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)

give z=/=y.

So

F(z-x-1)=F(x-x-1)+F(y-x-1) don't infer F(z-x-2)=F(x-x-2)+F(y-x-2)

So

F(z)=F(x)+F(y) don't infer F(z-1)=F(x-1)+F(y-1)

So

F(z)=F(x)+F(y) is not equivalent F(z-1)=F(x-1)+F(y-1)

So have two cases.

[F(x)+F(y)] = F(z) and F(x-1)+F(y-1)]=/=F(z-1)

or vice versa

So

[F(x)+F(y)]-[F(x-1)+F(y-1)]=/=F(z)-F(z-1).

Or

F(x)-F(x-1)+F(y)-F(y-1)=/=F(z)-F(z-1).

We have

F(x)-F(x-1) =[x(x+1)/2]^2 - [(x-1)x/2]^2.

=(x^4+2x^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.

So

x^3+y^3=/=z^3.

n>2. .Similar.

We have a string inference

G(z)*F(z)=G(x)*F(x)+G(y)*F(y) equivalent 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) infer 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) infer G(z)*F(z-x-2)=G(x)*F(x-x-2)+G(y)*F(y-x-2)

we see

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 )

give z=y.

and

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(y-x-2)

x>0 infer G(x)>0.

give z=/=y.

So

G(z)*F(z-x-1)=G(x)*F(x-x-1)+G(y-x-1)*F(y) don't infer G(z)*F(z-x-2)=G(x)*F(x-x-2)+G(y)*F(y-x-2)

So

G(z)*F(z)=G(x)*F(x)+G(y)*F(y) don't infer G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1)

So

G(z)*F(z)=G(x)*F(x)+G(y)*F(y) is not equiivalent G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1)

So have two cases

[G(x)*F(x)+G(y)*F(y)]=G(z)*F(z) and [ G(x)*F(x-1)+G(y)*F(y-1)]=/=G(z-1)*F(z-1)

or vice versa.

So

[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)].

Or

G(x)*[F(x) - F(x-1)] + G(y)*[F(y)-F(y-1)]=/=G(z)*[F(z)-F(z-1).]

We have

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) ]

So

x^n+y^n=/=z^n

Happy&Peace.

Trần Tấn Cường.

Study guides

☆☆

Q: When was Pierre De fermat's last theorem created?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

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.

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.

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

QED, Fermat's Last Theorem.

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.

Related questions

Andrew Wiles solved/proved Fermats Last Theorem. The theorem states Xn + Yn = Zn , where n represents 3, 4, 5,......... there is no solution.

The Last Theorem was created in 2008-07.

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.

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.

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.

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

He was a mathematician who contributed to the fields of calculus and algebra. His theorem an + bn = cn called, "Fermat's Last Theorem" was a challenge for the mathematical world to prove for a long time.

This was not the last theorem that Fermat wrote. Rather, it was the last one to be proven/disproven.

The Last Theorem has 311 pages.

QED, Fermat's Last Theorem.

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.

The ISBN of The Last Theorem is 978-0-00-728998-1.