MathNet 2008-part-04 — 165 problems (EN–VI) Question 60

Given a natural number $n$ greater than $1$, find all pairs of integers $a$ and $b$ such that the two equations $x^{n} + a x - 2008 = 0$ and $x^{n} + b x - 2009 = 0$ have at least one common real root.