A3. What is the largest natural number $n$ for which it is true that when the number $n$ is divided by 20, the remainder is equal to the quotient?

![](https://cdn.mathpix.com/cropped/2024_06_07_e347356273e0c1397da7g-02.jpg?height=400&width=390&top_left_y=1159&top_left_x=1526)
(A) 21
(B) 92
(C) 231
(D) 399
(E) 440

Problems for 1st year
A3. Let $k$ be the remainder and quotient when dividing the number $n$ by 20. Then $k \leq 19$ and $n=k \cdot 20+k=21 k$. Therefore, $n \leq 21 \cdot 19=399$. Checking $399=19 \cdot 20+19$ shows that the number $n=399$ satisfies the condition.