Exercise 2.
Suppose \(a\text{,}\) \(b\text{,}\) and \(c\) are integers. Prove that if \(a \mid b\) and \(a \mid c\) then \(a \mid b+c\) and \(a \mid b-c\text{.}\)
Suppose \(a\text{,}\) \(b\text{,}\) and \(c\) are integers. Prove that if \(a \mid b\) and \(a \mid c\) then \(a \mid b+c\) and \(a \mid b-c\text{.}\)