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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: $(a + c) - (b + d) = (a - b) + (c - d)$, and $n$ divides both terms.\nThe same holds for subtraction: $a - c \\equiv b - d \\pmod n$.\nTogether with [[compatibility with multiplication|072D5G4SK6]], this result shows that the addition of [[integers modulo n|01N3AYAA6N]] is well defined.\n\n## Explanations\n\n### L1 human\n\nTo find the remainder of a sum, you can add the remainders and reduce again.\nFor example, $17 \\equiv 2 \\pmod 5$ and $24 \\equiv 4 \\pmod 5$, so $17 + 24 = 41 \\equiv 2 + 4 = 6 \\equiv 1 \\pmod 5$.\n",
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