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The number of triplets (a, b, c) of posi...

The number of triplets (a, b, c) of positive integers satisfying the equation `|(a^(3)+1,a^(2)b,a^(2)c),(ab^(2),b^(3)+1,b^(2)c),(ac^(2),bc^(2),c^(3)+1)|=30` is equal to

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