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Let $K$ be an infinite field positive characteristic and $F(X,Y)\in K[[X,Y]]$. Assume that $F(Z_1+U_1,Z_2+U_2)=F(Z_1,Z_2)+F(U_1,U_2)$ where $Z_1,Z_2,U_1,U_2$ are twofour indeterminates. Can one assert that $F(X,Y)=G(X)+H(Y)$ with $G,H\in K[[X]]$?
Let $K$ be an infinite field positive characteristic and $F(X,Y)\in K[[X,Y]]$. Assume that $F(Z_1+U_1,Z_2+U_2)=F(Z_1,Z_2)+F(U_1,U_2)$ where $Z_1,Z_2,U_1,U_2$ are two indeterminates. Can one assert that $F(X,Y)=G(X)+H(Y)$ with $G,H\in K[[X]]$?
Let $K$ be an infinite field positive characteristic and $F(X,Y)\in K[[X,Y]]$. Assume that $F(Z_1+U_1,Z_2+U_2)=F(Z_1,Z_2)+F(U_1,U_2)$ where $Z_1,Z_2,U_1,U_2$ are four indeterminates. Can one assert that $F(X,Y)=G(X)+H(Y)$ with $G,H\in K[[X]]$?
Let $K$ be an infinite field positive characteristic and $F(X,Y)\in K[[X,Y]]$. Assume that $F(Z_1+U_1,Z_2+U_2)=F(Z_1,Z_2)+F(U_1,U_2)$ where $Z_1,Z_2,U_1,U_2$ are two indeterminates. Can one assert that $F(X,Y)=G(X)+H(Y)$ with $G,H\in K[[X]]$?
