Question 37
Let $a$, $b$, $c$ be distinct positive integers and let $r$, $s$, $t$ be positive integers such that:
$$
ab + 1 = r^2, \quad ac + 1 = s^2, \quad bc + 1 = t^2.$$
Prove that it is not possible that all three fractions $\frac{rs}{t}$, $\frac{rt}{s}$ and $\frac{st}{r}$ are positive integers. (Miljen Mikić)
$$
ab + 1 = r^2, \quad ac + 1 = s^2, \quad bc + 1 = t^2.$$
Prove that it is not possible that all three fractions $\frac{rs}{t}$, $\frac{rt}{s}$ and $\frac{st}{r}$ are positive integers. (Miljen Mikić)