Question 36
Let $a, b, c$ be integers such that
$$
\frac{ab}{c} + \frac{ac}{b} + \frac{bc}{a}
$$
is an integer.
Prove that each of the numbers
$$
\frac{ab}{c}, \quad \frac{ac}{b} \quad \text{and} \quad \frac{bc}{a}
$$
is an integer.
$$
\frac{ab}{c} + \frac{ac}{b} + \frac{bc}{a}
$$
is an integer.
Prove that each of the numbers
$$
\frac{ab}{c}, \quad \frac{ac}{b} \quad \text{and} \quad \frac{bc}{a}
$$
is an integer.