Question 72
Let $r$ be a rational number consider integers $a_1, a_2, \dots, a_6, b_1, b_2, \dots, b_6$ such that $1 \le b_1 \lt b_2 \lt \dots \lt b_6 \le 11$ and
$$
r = \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3} = \frac{a_4}{b_4} = \frac{a_5}{b_5} = \frac{a_6}{b_6}.
$$
Prove that $r$ is an integer.
$$
r = \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3} = \frac{a_4}{b_4} = \frac{a_5}{b_5} = \frac{a_6}{b_6}.
$$
Prove that $r$ is an integer.