Definition: When \(a\) and \(b\) are integers and \(a\) is nonzero, \(a\) divides \(b\) means there is an integer \(c\) such that \(b = ac\) . Symbolically, \(F(~(a,b)~) = \phantom{\exists c\in \mathbb{Z}~(b=ac)}\) and is a predicate over the domain Other (synonymous) ways to say that \(F(~(a,b)~)\) is true:
\(a\) is a factor of \(b\) \(a\) is a divisor of \(b\) \(b\) is a multiple of \(a\) \(a | b\)
When \(a\) is a positive integer and \(b\) is any integer, \(a | b\) exactly when \(b \textbf{ mod } a = 0\) When \(a\) is a positive integer and \(b\) is any integer, \(a | b\) exactly \(b = a \cdot (b \textbf{ div } a)\)