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  "body": "\n## Statement\n\nLet $F$ and $F'$ be [[finite fields|08RTDHX1SK]] with $|F| = |F'|$.\nThen $F$ and $F'$ are isomorphic.\n\n## Remarks\n\nThe proof: let $q = |F|$. Both fields have characteristic $p$ and prime subfield $\\mathbb{F}_p$. Both are [[splitting fields of $x^q - x$ over $\\mathbb{F}_p$|0CDAHW576M]], so they are isomorphic by the [[uniqueness of splitting fields|069A3BC3EP]].\nAlso, a field contains at most one subfield of order $q$: its elements must be the $q$ roots of $x^q - x$.\n\n## History\n\nE. H. Moore first proved the classification of finite fields in 1893.\n\n## Explanations\n\n### L1 human\n\nTwo finite fields with the same number of elements have the same structure.\nOnly the names of the elements can differ.\n",
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