4. Solve the following equation for positive $x$.

$$
x^{2014} + 2014^{2013} = x^{2013} + 2014^{2014}
$$
Answer: 2014.

Solution. Rewrite the equation in the following form $x^{2013}(x-1)=2014^{2013}(2014-1)$. The solution is $x=2014$. Since the function on the left, for $x>1$ this function is increasing, as the product of two positive increasing functions, the intersection with a constant function can be no more than one and one is already defined.

## Grading Criteria.

The solution is guessed: 0 points.