# Expanding A Tetration Expression!

Algebra Level 5

$\large \prod_{k=1}^{2016} \left (1 + z_k x^{11^k} \right) = 1 + a_1 x^{m_1} + a_2 x^{m_2} + \cdots + a_{2017} x^{m_{2017}} + \cdots + a_N x^{m_N}$

Consider the expansion above for $$z_k = e^{2k\pi i /11}$$, where $$a_1 <a_2 < a_3 < \cdots < a_N$$ and $$m_1 < m_2 < \cdots < m_N$$ are all constants.

If $$z_n =a_{2017}$$, find the minimum value of $$n$$.

Clarification: $$i=\sqrt{-1}$$.

×