Solve the system

$$
\begin{aligned}
& y^{2}=4 x^{3}+x-4 \\
& z^{2}=4 y^{3}+y-4 \\
& x^{2}=4 z^{3}+z-4
\end{aligned}
$$
The function $4 x^{3}+x-4$ is negative for $x \leq 0$, so all unknowns are positive. The function $4 x^{3}-x^{2}+x-4$ is increasing over the entire number line and equals zero at $x=1$. Therefore, if $x>1$, then $y^{2}=4 x^{3}+x-4>x^{2}$

> 1. Then, similarly, $z^{2}>x^{2}$ and

$x^{2}>z^{2}>y^{2}>x^{2}$, which is impossible. Similarly, the assumption $x<1$ leads to a contradiction.

## Answer

$(1,1,1)$.