4. (3 points) Does there exist a four-digit natural number with the sum of its digits being 23, which is divisible by 23?
Answer: Yes, for example $7682=23 \cdot 334$.

Solution: Generally speaking, the solution is contained in the answer, but let's explain how to find such a number. The sum of the digits of the product gives the same remainder when divided by 9 as the sum of the original numbers. Represent 23 as the difference between a multiple of 5 and a multiple of 9: $23=5 \cdot 10-3 \cdot 9$. Therefore, we need to find a three-digit multiplier with a digit sum of 10.

Here are all possible options: $1679,1886,3749,3956,4577,4784,4991,5198,5819,6647,6854$, $7268,7475,7682,8096,8717,8924,9338,9545,9752$.