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  "aliases": [
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  "body": "\n## Statement\n\nLet $a$ and $b$ be integers with $b \\neq 0$.\nThen there is exactly one pair of integers $(q, r)$ such that $a = b q + r$ and $0 \\le r \u003c |b|$.\n\n## Remarks\n\nThe integer $q$ is the quotient and the integer $r$ is the remainder of the division of $a$ by $b$.\nThe remainder is $0$ if and only if $b$ [[divides|096PW7Q014]] $a$.\nFor example, $-7 = 3 \\cdot (-3) + 2$, so the quotient of $-7$ by $3$ is $-3$ and the remainder is $2$.\n\n## Explanations\n\n### L1 human\n\nYou can share $a$ objects into groups of $b$ objects, with some objects left over.\nThe theorem says that the number of full groups and the rest are unique, if the rest is smaller than $|b|$.\nFor example, $17 = 5 \\cdot 3 + 2$: you get $3$ groups of $5$, and $2$ objects stay.\n",
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