# Difference between revisions of "Fermat's Last Theorem"

m (→The Theorem: Added display style) |
|||

Line 6: | Line 6: | ||

Given integers <math>a,b,c</math> and <math>n</math>, with <math>n \geq 3</math> there are no solutions to the equation: | 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>a^n + b^n = c^n</math> | + | <math>\displaystyle a^n + b^n = c^n</math> |

==See Also== | ==See Also== | ||

* [[Number Theory]] | * [[Number Theory]] | ||

** [[Diophantine Equations]] | ** [[Diophantine Equations]] |

## Revision as of 01:17, 23 June 2006

## 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 centuries. Finally, in 1993 Andrew Wiles produced a proof of the theorem - a proof that was much more complicated than anything Fermat could have produced himself.

## The Theorem

Given integers and , with there are no solutions to the equation: