Compare and Predict

Algebra Level 4

Let \(f\) be a function with domain \(\mathbb{R}\).

If \(f(x+2)\big(1-f(x)\big)=1+f(x)\) and \(f(1)=2016\), find the value of \(f(2017)\).

\(\)
Notation: \(\mathbb{R}\) denotes the set of real numbers.

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