An algebra problem by João Vitor

Algebra Level 5

Let \(P^{ 1 }\left( x \right) \) be the remainder of the polynomial \(p(x)={ (x-1) }^{ 2017 }\) when divided by another polynomial \(d(x)={ x }^{ 2 }-x+1\).

If we define \(P^{ k+1 }(x)={ P }^{ 1 }\left( P^k(x) \right) \) for every positive integer \(k\), evaluate \(P^{ 2017 }( 2016)\).

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Inspirations: PUC-Rio Maths Challenge and Harvard-MIT Tournament 2010 (General Test).
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