Many books define congruence modulo \(n\) slightly differently. They say that \(a \equiv b \pmod{n}\) if and only if \(n \mid a-b\text{.}\) In other words, two numbers are congruent modulo \(n\text{,}\) if their difference is a multiple of \(n\text{.}\) So which definition is correct? Turns out, it doesn't matter: they are equivalent.
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