Question 9
(HUN 1) For which positive integers $n$ do there exist two polynomials $f$ and $g$ with integer coefficients of $n$ variables $x_1,x_2,\ldots,x_n$ such that the following equality is satisfied:
$$\left(\sum_{i=1}^n x_i\right)f(x_1,x_2,\ldots,x_n)=g(x_1^2,x_2^2,\ldots,x_n^2)?$$
$$\left(\sum_{i=1}^n x_i\right)f(x_1,x_2,\ldots,x_n)=g(x_1^2,x_2^2,\ldots,x_n^2)?$$