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  "body": "\n## Definition\n\nLet $n$ be a positive integer, and let $a$ and $b$ be integers.\nThe integer $a$ is congruent to $b$ modulo $n$ when $n$ [[divides|096PW7Q014]] $a - b$.\nThe notation is $a \\equiv b \\pmod{n}$. The integer $n$ is the modulus of the congruence.\n\n## Remarks\n\nEquivalently, $a \\equiv b \\pmod n$ if and only if $a$ and $b$ have the same remainder on division by $n$, that is, $a \\bmod n = b \\bmod n$.\nCongruence modulo $n$ is an equivalence relation on the integers. Its classes are the [[residue classes|0QRV8FPK5M]] modulo $n$.\nFor example, $38 \\equiv 14 \\pmod{12}$, because $12 \\mid 24$.\nSome texts allow each integer $n$ as a modulus. Then congruence modulo $0$ is equality, and congruence modulo $-n$ is congruence modulo $n$.\n\n## Explanations\n\n### L1 human\n\nTwo integers are congruent modulo $n$ when they differ by a multiple of $n$.\nOn a $12$-hour clock, $14$ o'clock and $2$ o'clock show the same time, because $14 \\equiv 2 \\pmod{12}$.\n",
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