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  "body": "\n## Statement\n\nLet $n$ be a positive integer, and let $a$, $b$, $c$ and $d$ be integers.\nIf $a \\equiv b \\pmod n$ and $c \\equiv d \\pmod n$, then $a c \\equiv b d \\pmod n$.\n\n## Remarks\n\nThe proof: $a c - b d = a (c - d) + d (a - b)$, and $n$ divides both terms.\nWith [[compatibility with addition|00FWBN7F0Y]], this result shows that the multiplication of [[integers modulo n|01N3AYAA6N]] is well defined.\nBy induction, it gives [[compatibility with powers|0J5VGJYYC3]].\n\n## Explanations\n\n### L1 human\n\nTo find the remainder of a product, you can multiply the remainders and reduce again.\nFor example, the last digit of $27 \\cdot 43$ is the last digit of $7 \\cdot 3 = 21$, that is, $1$. This is the case $n = 10$.\n",
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  "name": "Congruence is compatible with multiplication",
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