A number theory problem by Wildan Bagus W. Hafidz

\[\large \begin{align} x & =2017-\frac { 2016 }{ 2017-\frac { 2016 }{ 2017-\frac { 2016 }{ \ddots } } } \\ x & =2016-\frac { 2015 }{ 2016-\frac { 2015 }{ 2016-\frac { 2015 }{ \ddots } } } \end{align}\]

Find the value of \(x\) that satisfies both the equations above.

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