2. Is $13^{2013}+13^{2014}+13^{2015}$ divisible by 61?
Answer: Yes, it is divisible.

Solution. Let's transform the given sum:

$$
13^{2013}+13^{2014}+13^{2015}=13^{2013} \cdot\left(1+13+13^{2}\right)=183 \cdot 13^{2013}=61 \cdot 3 \cdot 13^{2013}
$$

Thus, the given sum is divisible by 61.

## Grading Criteria.

- Correct solution - 7 points.
- The number $13^{2013}$ is factored out, but the number in parentheses is calculated incorrectly, and it is claimed that the expression is not divisible by $61,-2$ points.
- Only the answer "yes" is provided - 0 points.