Problem

Source: 2017 China Northern MO, Grade 11, Problem 1

Tags: algebra



Define sequence $(a_n):a_1=\text{e},a_2=\text{e}^3,\text{e}^{1-k}a_n^{k+2}=a_{n+1}a_{n-1}^{2k}$ for all $n\geq2$, where $k$ is a positive real number. Find $\prod_{i=1}^{2017}a_i$.