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  "body": "\n## Statement\n\nLet $n$ be a natural number with decimal digits $d_k d_{k-1} \\dots d_0$, so that $n = \\sum_{i=0}^{k} d_i 10^i$.\nThen $9 \\mid n$ if and only if $9 \\mid d_0 + d_1 + \\dots + d_k$.\n\n## Remarks\n\nMore precisely, $n \\equiv d_0 + d_1 + \\dots + d_k \\pmod 9$, because $10^i \\equiv 1 \\pmod 9$ for each $i$.\nFor example, $9 \\mid 81{,}243$, because $8 + 1 + 2 + 4 + 3 = 18$.\nThe congruence is the basis of [[casting out nines|0E7W0EM6J6]].\n\n## Explanations\n\n### L1 human\n\nAdd the digits. The number is a multiple of $9$ exactly when the sum is a multiple of $9$.\nFor example, $123{,}456$ has the digit sum $21$, which is not a multiple of $9$. So $9 \\nmid 123{,}456$.\n",
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