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Soient \(a_1, \dots, a_n \in \N^{*}\) et \(b_i = \prod_{j \ne i} a_j\).
Montrer que :
\(\text{pgcd}( a_1, \dots, a_n ) \times \text{ppcm}( b_1, \dots, b_n) =
\text{ppcm}( a_1, \dots, a_n ) \times \text{pgcd}( b_1, \dots, b_n) =
\prod a_i\).