Question 129
Initially $n \gt 1$ positive integers are written on the board. On each minute, a new number that is the sum of squares of all already written numbers appears on the board. (For example, if initial numbers were $1$, $2$, $2$, then on the first minute the number $1^2 + 2^2 + 2^2$ appears.) Prove that the $100$th new number has at least $100$ different prime divisors.