Abstract
It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics, it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.
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