Let $a_1, a_2, ..., a_{2004}$ be integer numbers such that for all positive integers $n$ the number $A_n = a^n_1 + a^n_2 + ...+ a^n_{2004}$ is a perfect square. What is the minimal number of zeros within the $2004$ numbers?
Source:
Tags: number theory, 3rd edition
Let $a_1, a_2, ..., a_{2004}$ be integer numbers such that for all positive integers $n$ the number $A_n = a^n_1 + a^n_2 + ...+ a^n_{2004}$ is a perfect square. What is the minimal number of zeros within the $2004$ numbers?