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  "body": "\n## Definition\n\nA finite field is a [[field|0QA8CHH8MG]] $F$ whose underlying set is finite.\nThe order of $F$ is its number of elements $|F|$.\n\n## Remarks\n\nFor each prime number $p$, the ring $\\mathbb{Z}/p\\mathbb{Z}$ is a [[finite field|0NV6E43P4A]] of order $p$.\nThe [[order of a finite field is a prime power|0H5WWC8RZX]] $p^n$, where $p$ is the characteristic.\nThe field $\\mathbb{F}_2[x]/(x^2 + x + 1)$ is a finite field of order $4$. It is not $\\mathbb{Z}/4\\mathbb{Z}$, which is not a field.\nFinite fields are used in number theory, algebraic geometry, cryptography and coding theory.\n\n## Explanations\n\n### L1 human\n\nA finite field is a finite set where you can add, subtract, multiply and divide by nonzero elements, with the usual rules.\nThe simplest ones are the integers modulo a prime.\n",
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