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For the polynomials \(A_1 = X^2\), \(A_2 = X^2 + 1\), \(A_3 = X^2 - 1\) in \(\mathbb{R}[X]\), compute the three pairwise gcds and the three-set gcd \(A_1 \wedge A_2 \wedge A_3\). Conclude on the relationship between « pairwise coprime » and « coprime as a set » in this case.
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