The corresponding expression was valid for two variables as well (it suffices to set "X"3 to zero), but since it involves "p"3, it could not be used to illustrate the statement for "n" = 2. The example shows that whether or not the expression for a given monomial symmetric polynomial in terms of the first "n" power sum polynomials involves rational coefficients may depend on "n". But rational coefficients are "always" needed to express elementary symmetric polynomials (except the constant ones, and "e"1 which coincides with the first power sum) in terms of power sum polynomials. The Newton identities provide an explicit method to do this; it involves division by integers up to "n", which explains the rational coefficients. Because of these divisions, the mentioned statement fails in general when coefficients are taken in a field of finite characteristic; however it is valid with coefficients in any ring containing the rational numbers.