ÖMO 1985 Problem 4

Find all natural numbers $n$ such that the equation:

$a_{n+1} x^2-2x \sqrt{a_1^2+a_2^2+...+a_{n+1}^2}+a_1+a_2+...+a_n=0$

has real solutions for all real numbers $a_1,a_2,...,a_{n+1}$ .