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  "body": "\n## Example\n\nLet $n$ be a positive integer.\nThe integers modulo $n$, $\\mathbb{Z}/n\\mathbb{Z} = \\{0, 1, \\ldots, n - 1\\}$, with addition modulo $n$, form a [[cyclic group|0KVGH0J5B3]] of [[order|0B85S2V2DR]] $n$.\nThe residue $1$ generates it, because each residue $k$ is the sum of $k$ copies of $1$.\nEach cyclic group of order $n$ is isomorphic to $\\mathbb{Z}/n\\mathbb{Z}$, and this group is often written $C_n$.\n\n## Remarks\n\nA residue $k$ generates $\\mathbb{Z}/n\\mathbb{Z}$ exactly when $\\gcd(k, n) = 1$.\nThe [[group of $n$th roots of unity|0WX11EA3F3]] is a cyclic group of order $n$ in multiplicative notation.\nThe rotations of a regular $n$-gon also form a cyclic group of order $n$.\n\n## Explanations\n\n### L1 human\n\nThink of a clock with $n$ hours, where you add hours and wrap around after $n$.\nThis clock arithmetic gives the cyclic group of order $n$.\nEvery cyclic group of order $n$ looks the same as this clock, up to the names of the elements.\n",
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