2. Three integers are written in a row $a, b, c$. Below these numbers, in the second row, the numbers $a-b, b-c, c-a$ are written. The numbers in the third row and subsequent rows are formed from the numbers of the previous row according to the same rule. Is it possible to encounter the number 2021 among the numbers in the rows below the 13th row?
Answer: impossible.

Solution.

Let's write down several rows according to the condition of the problem:

| $a$ | $b$ | $c$ |
| :---: | :---: | :---: |
| $a-b$ | $b-c$ | $c-a$ |
| $a-2 b+c$ | $b-2 c+a$ | $c-2 a+b$ |
| $3(c-b)$ | $3(a-c)$ | $3(b-a)$ |
| $3(c-b)-3(a-c)$ | $3(a-c)-3(b-a)$ | $3(b-a)-3(c-b)$ |
| $\cdots$ | $\cdots$ | $\cdots$ |

All numbers of the following rows are multiples of three, as they are differences of numbers that are multiples of three.

The number 2021 is not a multiple of three, so from the third row onward, it cannot appear in the sequence of numbers.