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The assertion that the equation x^n + y^n = z^n has no solutions in non-zero integers x,y,z when n > 2.
The equation was originally proposed by Fermat in the margin of his copy of the works of Diophantus in 1605, who claimed to have a proof which, famously, 'the margin was too small to contain'.
It was proved by Andrew Wiles in a proof announced in 1993 and completed with Richard Taylor in 1994.
The proof deduces the result as a consequence of the proof of the deeper Shimura-Taniyama-Weil conjecture on elliptic curves over the rational numbers.
Attempts to prove Fermat's Last Theorem in the 19th century led to the development of much of modern algebraic number theory.
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