Task B-3.1. Solve the equation

$$
\left(4-\frac{x}{2013}\right)^{10^{2013}}=\left(\frac{x}{671}\right)^{10^{2013}}
$$
## Solution.

The number $10^{2013}$ is even. Then we have

$$
4-\frac{x}{2013}=\frac{x}{671} \quad \text { or } \quad 4-\frac{x}{2013}=-\frac{x}{671}
$$

From the first equation, $\frac{x}{3 \cdot 671}+\frac{x}{671}=4$, which simplifies to

$$
\frac{4 x}{2013}=4, \quad x=2013
$$

Similarly, from the second equation, we get $\frac{-2 x}{2013}=4$.

This leads to the second solution $x=-4026$.

Therefore, the solutions to the equation are the numbers -4026 and 2013.