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 2023 among the numbers in the rows below the 15th 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 in the following rows are multiples of three, as they are differences of numbers that are multiples of three.

The number 2023 is not a multiple of three, so from the third row onward, it cannot appear in the sequence of numbers.