[ Identical Transformations ]

It is known that $a^{2}+b=b^{2}+c=c^{2}+a$. What values can the expression $a\left(a^{2}-b^{2}\right)+b\left(b^{2}-c^{2}\right)+c\left(c^{2}-\right.$ $\left.a^{2}\right)$ take?
From the condition, it follows that $a^{2}-b^{2}=c-b, b^{2}-c^{2}=a-c$ and $c^{2}-a^{2}=b-a$. Therefore, $a\left(a^{2}-b^{2}\right)+b\left(b^{2}-c^{2}\right)+$ $c\left(c^{2}-a^{2}\right)=a(c-b)+b(a-c)+c(b-a)=0$.

## Answer

0.