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  "body": "\n## Definition\n\nLet $n$ be a positive integer.\nA complete residue system modulo $n$ is a set $S$ of integers that contains exactly one element of each [[residue class|0QRV8FPK5M]] modulo $n$.\n\n## Remarks\n\nEquivalently, $S$ has exactly $n$ elements, and no two distinct elements of $S$ are congruent modulo $n$.\nThe set $\\{0, 1, \\dots, n - 1\\}$ is the set of the least nonnegative residues. It is a complete residue system modulo $n$.\nFor odd $n$, the set $\\{ -\\tfrac{n-1}{2}, \\dots, -1, 0, 1, \\dots, \\tfrac{n-1}{2} \\}$ of the least absolute residues is also a complete residue system.\nIf $S$ is a complete residue system modulo $n$ and $\\gcd(a, n) = 1$, then $\\{ a s + b : s \\in S \\}$ is also a complete residue system for each integer $b$.\n\n## Explanations\n\n### L1 human\n\nA complete residue system picks one representative from each box of the integers modulo $n$.\nFor $n = 4$, both $\\{0, 1, 2, 3\\}$ and $\\{4, -3, 10, 7\\}$ are complete residue systems.\n",
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