Question 65
Find the smallest positive integer $k$ for which the 100 fractions
$$
\frac{50}{k+49}, \frac{50}{k+51}, \frac{51}{k+50}, \frac{51}{k+52}, \dots, \frac{99}{k+98}, \frac{99}{k+100}
$$
are irreducible.
$$
\frac{50}{k+49}, \frac{50}{k+51}, \frac{51}{k+50}, \frac{51}{k+52}, \dots, \frac{99}{k+98}, \frac{99}{k+100}
$$
are irreducible.