# 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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