# 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 | + | 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. |

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==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 with , there are no solutions to the equation:

## 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.