1. Ana has three stamp albums. In the first one, there is one fifth of the stamps, in the second one, there are several sevenths, and in the third one, there are 303 stamps. How many stamps does Ana have?
Solution: Let Ana have a total of $x$ stamps, $x \in N$; then in the first album, she has $\frac{1}{5} x$, in the second $\frac{k}{7} x, k \in N$, and in the third album, 303 stamps. Therefore, we have $\frac{x}{5}+\frac{k x}{7}+303=x$. From this, $x=\frac{35 \cdot 303}{28-5 k}$. For $x$ to be a natural number, $k$ must be odd. From 28-5k>0, it follows that $k \in\{1,3,5\}$. By checking, we confirm that only for $\mathrm{k}=5$, $x$ is a natural number and in this case $\mathrm{x}=3535$. Therefore, Ana had a total of 3535 stamps.