\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(a, b \in \mathbb{Z}^*\) with \(a \wedge b = 1\). Show that \((a + b) \wedge (a b) = 1\). Hint. Show that any common prime divisor of \(a + b\) and \(a b\) is also a common divisor of \(a\) and \(b\).
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