2010 IMO Shortlist N3

Find the smallest number $n$ such that there exist polynomials $f_{1}, f_{2}, \ldots, f_{n}$ with rational coefficients satisfying $$x^{2}+7=f_{1}(x)^{2}+f_{2}(x)^{2}+\cdots+f_{n}(x)^{2} .$$ (Poland) Answer. The smallest $n$ is 5 .

找到最小数 $n$，使得存在多项式 $f_{1}, f_{2}, \ldots, f_{n}$，其有理系数满足 $$x^{2}+7=f_{1}(x)^{2}+f_{2}(x)^{2}+\cdots+f_{n}(x)^{2} 。$$(波兰)答案。最小的 $n$ 是 5 。