Find the smallest number
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that there exist polynomials
![f_1, f_2, \ldots , f_n](/media/m/1/4/4/144245d04b6757955e12a8e832b3c556.png)
with rational coefficients satisfying
![x^2+7 = f_1\left(x\right)^2 + f_2\left(x\right)^2 + \ldots + f_n\left(x\right)^2.](/media/m/2/4/c/24c9e4d21cf742431ceeefcd82f8b036.png)
Proposed by Mariusz Skałba, Poland
%V0
Find the smallest number $n$ such that there exist polynomials $f_1, f_2, \ldots , f_n$ with rational coefficients satisfying $$x^2+7 = f_1\left(x\right)^2 + f_2\left(x\right)^2 + \ldots + f_n\left(x\right)^2.$$
Proposed by Mariusz Skałba, Poland