Number theory Diophantine equations Theorem

Fermat's Last Theorem

Statement

Let $n$ be an integer with $n > 2$ . Then there are no positive integers $a$ , $b$ and $c$ with $a^n + b^n = c^n$ .

Remarks

For $n = 2$ there are infinitely many solutions, the Pythagorean triples. It is enough to prove the theorem for $n = 4$ and for each odd prime $n$ , because each $n > 2$ has one of these as a divisor. The cases n = 4 and n = 3 have elementary proofs.

History

Pierre de Fermat stated the theorem around 1637 and wrote that he had a proof. Andrew Wiles gave the first proof in 1994, with a step completed jointly with Richard Taylor. The proof was published in 1995. The proof uses the modularity of semistable elliptic curves.

Reading path

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Diophantine equation concept
Fermat's Last Theorem statement

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Regular prime

Tag	`0Y5X3SDBCZ`
URI	`m2://0Y5X3SDBCZ`
Aliases	`flt`
Kind	statement, theorem
Writing	W1 stated
MSC	11D41
Status	This copy of the site has no build data. Run `m2 status 0Y5X3SDBCZ`.
Uses	Diophantine equation
Same as	Wikidata Q132469 Wikipedia Fermat's Last Theorem

Fermat's Last Theorem

Statement

Remarks

History

Reading path

Where this leads

Further reading

What this page needs for W2

What links here

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