Question 102
Let $n \geq 1$ be a positive integer. A permutation $(a_{1}, a_{2}, \ldots, a_{n})$ of the numbers $(1,2, \ldots, n)$ is called quadratique if among the numbers $a_{1}, a_{1}+a_{2}, \ldots, a_{1}+a_{2}+\ldots+a_{n}$ there exists at least one perfect square. Find the greatest number $n$, which is less than $2003$, such that every permutation of the numbers $(1,2, \ldots, n)$ will be quadratique.