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  "body": "\n## Definition\n\nLet $n$ be a positive integer and let $q$ be an integer.\nThen $q$ is a quadratic residue modulo $n$ if there is an integer $x$ with $x^2 \\equiv q \\pmod n$.\nOtherwise $q$ is a quadratic nonresidue modulo $n$.\n\n## Remarks\n\nMany texts also require $\\gcd(q, n) = 1$, and so they do not count $0$ as a quadratic residue.\nModulo $7$, the squares of $1, \\dots, 6$ are $1, 4, 2, 2, 4, 1$. So the nonzero quadratic residues modulo $7$ are $1$, $2$ and $4$.\nModulo an odd prime $p$, exactly $(p - 1)/2$ of the classes $1, \\dots, p - 1$ are quadratic residues.\nThe product of two quadratic residues is a quadratic residue.\n\n## Explanations\n\n### L1 human\n\nA quadratic residue modulo $n$ is a number that is a perfect square in the arithmetic modulo $n$.\nFor example, $2$ is not a square in the integers, but $3^2 = 9 \\equiv 2 \\pmod 7$. So $2$ is a quadratic residue modulo $7$.\n",
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