Galperin G.A.

Solve the equation in natural numbers: $x+\frac{1}{y+\frac{1}{z}}=\frac{10}{7}$.
The second term is positive but less than one. Since $10 / 7=1+3 / 7$, then $x=1$, and $y+1 / z=7 / 3=2+1 / 3$. By the same reasoning, $y=2, z=3$.

## Answer

$$
x=1, y=2, z=3
$$

Let $\alpha$ be a positive real number, and $d$ be a natural number.

Prove that the number of natural numbers not exceeding $\alpha$ and divisible by $d$ is $[\alpha / d]$.