Question 37
Determine integers $a$, $b$ and $c$ such that the polynomials
$$
P(x) = x^9 - x^7 - 31x^2 - 26x - 17 \quad \text{and} \quad Q(x) = x^{13} - x^{11} - a x^2 - b x - c
$$
have a common factor.
$$
P(x) = x^9 - x^7 - 31x^2 - 26x - 17 \quad \text{and} \quad Q(x) = x^{13} - x^{11} - a x^2 - b x - c
$$
have a common factor.