solution of function containing two variables

Question

If $f(x,y)=10^5x^5+50000x^4y+10^4x^3y^2+10^3x^2y^3+50xy^4$, then is it possible that $f(x_1,y_1)=f(x_2,y_2)$ for $x_1\neq x_2$ and $y_1\neq y_2$ for all x,y belongs to Z+?

Answer 1

Yes, the polynomial does not have to be one-to-one.

For example $$ f(x,y)=x^5-5x^4y $$ have solutions $$ f(0,0)=f(5,1)=0$$