Difference between revisions of "Fermat's Last Theorem"

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'''Fermat's Last Theorem''' is a long-unproved theorem stating that for integers <math>\displaystyle a,b,c,n</math> with <math>n \geq 3</math>, there are no solutions to the equation: <math>\displaystyle a^n + b^n = c^n</math>
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==History==
 
==History==
Fermat's last theorem is particularly famous in number theory.  It was proposed by Fermat in the margin of his book Arithmetica.  The note in the margin (when translated) read: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."  However, nobody was able to prove this theorem for centuriesFinally, in 1993 Andrew Wiles produced a proof of the theorem - a proof that was much more complicated than anything Fermat could have produced himself.
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Fermat's last theorem was proposed by [[Pierre Fermat]] in the margin of his book ''Arithmetica''.  The note in the margin (when translated) read: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."  Despite Fermat's claim that a simple proof existed, the theorem wasn't proven until [[Andrew Wiles]] did so in 1993Interestingly enough, Wiles's proof was much more complicated than anything Fermat could have produced himself.
 
 
==The Theorem==
 
 
 
Given integers <math>a,b,c</math> and <math>n</math>, with <math>n \geq 3</math> there are no solutions to the equation:
 
 
 
<math>\displaystyle a^n + b^n = c^n</math>
 
  
 
==See Also==
 
==See Also==
 
* [[Number Theory]]
 
* [[Number Theory]]
 
** [[Diophantine Equations]]
 
** [[Diophantine Equations]]

Revision as of 17:44, 23 June 2006

Fermat's Last Theorem is a long-unproved theorem stating that for integers $\displaystyle a,b,c,n$ with $n \geq 3$, there are no solutions to the equation: $\displaystyle a^n + b^n = c^n$

History

Fermat's last theorem was proposed by Pierre Fermat in the margin of his book Arithmetica. The note in the margin (when translated) read: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Despite Fermat's claim that a simple proof existed, the theorem wasn't proven until Andrew Wiles did so in 1993. Interestingly enough, Wiles's proof was much more complicated than anything Fermat could have produced himself.

See Also

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