GR-HMS 2017 Problem 4

Let $u$ be the positive root of the equation $x^2+x-4=0$ . The polynomial $$P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0$$ where $n$ is positive integer has non-negative integer coefficients and $P(u)=2017$ .

1. Prove that $a_0+a_1+...+a_n\equiv 1\mod 2$ .
2. Find the minimum possible value of $a_0+a_1+...+a_n$ .