Practice! #4

Algebra Level 4

\[\large \begin{cases} a^{2}+b^{2}=c^{2} \\ \dfrac{ab}{2}=a+b+c \end{cases} \]

Positive integers \(a\), \(b\) and \(c\), where \(a<b<c\), satisfy the system of equations above. If there are \(n\) triplets \((a,b,c)\) then enter \(\displaystyle\sum_{k=1}^{n} (a_{k} + b_{k} + c_{k})\) as your answer.

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