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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:

\sum_{i=1}^n x_i f(x_1, x_2, \ldots , x_n) = g(x_1^2, x_2^2, \ldots , x_n^2) \ ?

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