Waring's problem for polynomials in two variables

Arnaud Bodin, Mireille Car

We prove that all polynomials in several variables can be decomposed as the sums of $k$th powers: $P(x_1,...,x_n)=Q_1(x_1,...,x_n{)}^k+...+Q_s(x_1,...,x_n{)}^k$, provided that eleme…