Vietnam TST 2004
Posted: Fri May 18, 2012 11:48 pm
Find all real numbers $\alpha$ for which there is a unique function $f:\mathbb R\mapsto \mathbb R$ satisfying
\[f(x^{2}+y+f(y))=f(x)^{2}+\alpha y\]
for all real $x,y$.
\[f(x^{2}+y+f(y))=f(x)^{2}+\alpha y\]
for all real $x,y$.