<s>[INST] To prove the irrationality of e, Lindemann proves the following: Suppose that the real numbers $a_0, a_1, \ldots, a_n, b_1, \ldots, b_n$ satisfy $a_0 = 1$ and $a_k \neq 0$ and $b_k \neq 0$ for all $k$, and
\[\sum_{k=0}^n a_k b_1^{k} b_2^{k} \cdots b_n^k = 0\]
If we can show that this equation is impossible, then we will have shown that e is irrational.
What is the value of $n$ that makes this equation impossible?[/INST]