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  "body": "\n## Statement\n\nLet $n$ be a natural number.\nThen $n = x^2 + y^2 + z^2$ for some integers $x$, $y$ and $z$ if and only if $n \\neq 4^a (8b + 7)$ for all natural numbers $a$ and $b$.\n\n## Remarks\n\nThe \"only if\" part is easy: a square is $0$, $1$ or $4$ modulo $8$, so no sum of three squares is $7$ modulo $8$.\nThe first numbers that are not sums of three squares are $7$, $15$, $23$, $28$ and $31$.\nThe theorem implies [[Lagrange's four-square theorem|0KYYSMEVHH]] in a few lines.\n\n## History\n\nLegendre gave the first proof in 1797 or 1798.\nGauss proved a more general result in 1801.\n\n## Explanations\n\n### L1 human\n\nMost numbers are sums of three squares, for example $6 = 4 + 1 + 1$.\nThe exceptions are $7, 15, 23, \\dots$, the numbers that leave remainder $7$ on division by $8$, and these numbers times powers of $4$.\n",
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