Question 29
Let $\xi$ be the positive root of the equation $x^2 + x - 4 = 0$. The polynomial $P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$, where $n$ is a positive integer, has nonnegative integer coefficients and $P(\xi) = 2017$.
(i) Prove that: $a_0 + a_1 + \dots + a_n \equiv 1 \pmod{2}$
(ii) Find the least possible value of the sum: $a_0 + a_1 + \dots + a_n$.
(i) Prove that: $a_0 + a_1 + \dots + a_n \equiv 1 \pmod{2}$
(ii) Find the least possible value of the sum: $a_0 + a_1 + \dots + a_n$.