4. Two natural numbers add up to 2015. If one of them is divided by the other with a remainder, the quotient is 25. Find all pairs of such numbers (and prove that there are no others).
4. Answer. $x=1938, y=77$.

Let these numbers be $x$ and $y$. Then $x+y=2015$ and $x=25 y+s$, where $s$ is the remainder. We get that $x+y=$ $26 y+s=2015.26 y=2015-s$. From the inequality $0 \leq s \leq 24$ we obtain

$$
\begin{gathered}
2015-24 \leq 26 y \leq 2015, \text { or } \\
76.5<y<77.5
\end{gathered}
$$

Thus, $y=77, \mathrm{a} x=1938$.