Excel in math, science, and engineering

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Let \(a\),\(b\),\(c\) be positive integers such that \(a\),\(b\),\(c\) \(>1\) and: \(a\mid bc+1 ,\) \(c\mid ab+1 ,\)\(b\mid ac+1 ,\) , if \((a_i ,b_i,c_i)\) are solutions find: \(\sum (a_i + b_i +c_i) \).

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