Maclaurin 2026 — Six integers and nested linear expressions

From the set $\{1, 2, 3, \ldots, n\}$, six different integers $A, B, C, D, E, F$ are chosen so that the following equation holds for all values of $x$:

(a) Show that for $n = 9$ this is possible.

(b) Prove that this is not possible for $n = 8$.