\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For \(A = X^5 + 1\) and \(B = X^3 + 1\) in \(\mathbb{R}[X]\), compute \(A \wedge B\) and a Bézout pair \((U, V)\) via the extended Euclidean algorithm.
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