25. In triangle $ABC$, the altitude $BH$ is drawn, point $O$ is the center of the circumscribed circle around it, and the length of its radius is $R$. Find the measure in radians of the largest of the angles $ACB$ and $BAC$, given that $R=(5 / 8) \cdot B H=(5 / 6) \cdot O H$. If necessary, round the found value to two decimal places.
Answer: 1.82.

V. For their summer vacation, the residents of Flower City, Znayka and Neznayka, stayed in a large 15-story hotel by the sea. Znayka noticed that the sum of all room numbers from the first to his own, inclusive, is twice the sum of all room numbers from the first to the one where Neznayka stayed, inclusive. All rooms in the hotel are numbered consecutively from 1 to 1599, and Znayka lives in a room with a number greater than 200. Determine the room number where Znayka is staying.

If there are several room numbers, write their sum in the answer. If there are no such room numbers, write the number 0.

Solution. According to the problem, the room number of Neznayka $k$ and the room number of Znayka $n$ satisfy the relation $n^{2}+n=2\left(k^{2}+k\right)$. After substituting $x=2 k+1, y=2 n+1$, this relation simplifies to

$$
2 x^{2}-y^{2}=1
$$

The construction of all natural solutions to the equation is based on the following elementary considerations.