Question 73
Determine all pairs $(a, b)$, of non-negative integers such that the quotients
$$
\frac{3a + 8b + 2}{10a + 2b + 1} \quad \text{and} \quad \frac{8a + b + 3}{2a + 7b + 3}
$$
are integers simultaneously.
$$
\frac{3a + 8b + 2}{10a + 2b + 1} \quad \text{and} \quad \frac{8a + b + 3}{2a + 7b + 3}
$$
are integers simultaneously.