## Task B-2.4.

Solve the equation in the set of integers

$$
x^{8}+y^{2016}=32 x^{4}-256
$$
## Solution.

$$
\begin{aligned}
x^{8}+y^{2016} & =32 x^{4}-256 \\
y^{2016} & =-x^{8}+32 x^{4}-256 \\
y^{2016} & =-\left(x^{4}-16\right)^{2}
\end{aligned}
$$

The left side of the equation is $\geqslant 0$, while the right side is $\leqslant 0$.

$$
\begin{gathered}
y^{2016}=0 \quad \Rightarrow \quad y=0 \\
x^{4}-16=0 \quad \Rightarrow \quad x_{1,2}= \pm 2, \quad x_{3,4}= \pm 2 i
\end{gathered}
$$

We are looking for integer solutions, so the final solutions are $(2,0)$ and $(-2,0)$.