Find all nonnegative real number $a$, such that $f(a)=0$ for any function $f$ satisfying: $xf(1+xf(y))=f(f(x)+f(y))$ with all $x,y$ are nonnegative real number.
I don't know why this problem only ask the number $a$ for $f(a)=0$ instead of the function $f(x)$. Is there any special thing here? Is it possible to show the bijection? I will show what I get from trying to solve this: $f(f(x)+f(0))=f(1+xf(0))=0$. How to find $t=f(0)$, show me your solution or any idea please, thank all.