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  "body": "\n## Statement\n\nLet $n$ be an integer with $n \u003e 2$.\nThen there are no positive integers $a$, $b$ and $c$ with $a^n + b^n = c^n$.\n\n## Remarks\n\nFor $n = 2$ there are infinitely many solutions, the [[Pythagorean triples|01G1WY1GVX]].\nIt is enough to prove the theorem for $n = 4$ and for each odd prime $n$, because each $n \u003e 2$ has one of these as a divisor.\nThe cases [[n = 4|0E741HSMJ1]] and [[n = 3|07NKG38VEG]] have elementary proofs.\n\n## History\n\nPierre de Fermat stated the theorem around 1637 and wrote that he had a proof.\nAndrew Wiles gave the first proof in 1994, with a step completed jointly with Richard Taylor. The proof was published in 1995.\nThe proof uses the modularity of semistable elliptic curves.\n\n## Explanations\n\n### L1 human\n\nThe equation $a^2 + b^2 = c^2$ has many whole-number solutions, such as $3^2 + 4^2 = 5^2$.\nFor cubes, fourth powers and all higher powers, the theorem says that there are none.\nThe statement is simple, but the proof took more than 350 years.\n",
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